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alternate case: n+1

Fibonacci sequence (12,811 words) [view diff] exact match in snippet view article find links to article

n + 1 − F m + 1 F n = ( − 1 ) n F m − n {\displaystyle F_{m}F_{n+1}-F_{m+1}F_{n}=(-1)^{n}F_{m-n}} F 2 n = F n + 1 2 − F n1 2 = F n ( F n + 1 + F n
Standard deviation (7,607 words) [view diff] no match in snippet view article find links to article
replacing N − 1 with N − 1.5, yielding: σ ^ = 1 N1.5 ∑ i = 1 N ( x i − x ¯ ) 2 , {\displaystyle {\hat {\sigma }}={\sqrt {{\frac {1}{N-1.5}}\sum
Pi (17,500 words) [view diff] no match in snippet view article find links to article
n = 1 ∞ 1 n k ( a q n1 + b q 2 n1 + c q 4 n1 ) , {\displaystyle \pi ^{k}=\sum _{n=1}^{\infty }{\frac {1}{n^{k}}}\left({\frac {a}{q^{n}-1}}+{\frac
Taylor series (8,236 words) [view diff] no match in snippet view article find links to article
x n + 1 n ! = 1 + ∑ n = 1 ∞ x n n ! + ∑ n = 0 ∞ x n + 1 n ! = 1 + ∑ n = 1 ∞ x n n ! + ∑ n = 1 ∞ x n ( n1 ) ! = 1 + ∑ n = 1 ∞ ( 1 n ! + 1 ( n1 )
Variance (10,005 words) [view diff] no match in snippet view article find links to article
the denominator are n, n − 1, n + 1, and n − 1.5: n is the simplest (the variance of the sample), n − 1 eliminates bias, n + 1 minimizes mean squared
Binomial distribution (7,339 words) [view diff] no match in snippet view article find links to article
n + 1 ) p ⌋ if  ( n + 1 ) p  is 0 or a noninteger , ( n + 1 ) p    and    ( n + 1 ) p − 1 if  ( n + 1 ) p ∈ { 1 , … , n } , n if  ( n + 1 ) p = n + 1
Normal distribution (22,254 words) [view diff] no match in snippet view article find links to article
distribution with (n1) degrees of freedom: s 2 ∼ σ 2 n1 ⋅ χ n1 2 , σ ^ 2 ∼ σ 2 n ⋅ χ n1 2 . {\displaystyle s^{2}\sim {\frac {\sigma ^{2}}{n-1}}\cdot \chi
Prime number (14,098 words) [view diff] no match in snippet view article find links to article
factors divides both n and ( n1 ) ! {\displaystyle (n-1)!} , and so ( n1 ) ! ≡ − 1 ( mod n ) {\displaystyle (n-1)!\equiv -1{\pmod {n}}} is impossible
Round-robin tournament (3,305 words) [view diff] no match in snippet view article find links to article
( n1 ) {\displaystyle (n-1)} , then subtract ( n1 ) {\displaystyle (n-1)} from the sum. This schedule can also be represented as a (n-1, n-1) table
Golden ratio (12,981 words) [view diff] no match in snippet view article find links to article
n = φ n1 + φ n − 3 + ⋯ + φ n1 − 2 m + φ n − 2 − 2 m φ n − φ n1 = φ n − 2 . {\displaystyle {\begin{aligned}\varphi ^{n}&=\varphi ^{n-1}+\varphi
Rational number (3,516 words) [view diff] no match in snippet view article find links to article
( m 1 , n 1 ) + ( m 2 , n 2 ) ≡ ( m 1 n 2 + n 1 m 2 , n 1 n 2 ) , {\displaystyle (m_{1},n_{1})+(m_{2},n_{2})\equiv (m_{1}n_{2}+n_{1}m_{2},n_{1}n_{2}),}
E (mathematical constant) (6,151 words) [view diff] no match in snippet view article
series e = ∑ n = 0 ∞ 1 n ! = 1 + 1 1 + 1 1 ⋅ 2 + 1 1 ⋅ 2 ⋅ 3 + ⋯ . {\displaystyle e=\sum \limits _{n=0}^{\infty }{\frac {1}{n!}}=1+{\frac {1}{1}}+{\frac
Polynomial (8,042 words) [view diff] no match in snippet view article find links to article
polynomial n a n x n1 + ( n1 ) a n1 x n − 2 + ⋯ + 2 a 2 x + a 1 = ∑ i = 1 n i a i x i − 1 . {\displaystyle na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\dots
List of trigonometric identities (12,067 words) [view diff] no match in snippet view article find links to article
n1 ) x ) sin ⁡ x {\displaystyle {\begin{aligned}\cos((n-1)x+x)&=\cos((n-1)x)\cos x-\sin((n-1)x)\sin x\\\cos((n-1)x-x)&=\cos((n-1)x)\cos x+\sin((n-1)x)\sin
5 (12,152 words) [view diff] no match in snippet view article find links to article
form 2 2 n + 1 {\displaystyle 2^{2^{n}}+1} , and more generally the second Sierpiński number of the first kind, n n + 1 {\displaystyle n^{n}+1} . There
Weighted arithmetic mean (8,987 words) [view diff] no match in snippet view article find links to article
^ pwr ) = 1 n 1 n1 ∑ i = 1 n ( y i p i − Y ^ p w r ) 2 = 1 n 1 n1 ∑ i = 1 n ( n n y i p i − n n ∑ i = 1 n w i y i ) 2 = 1 n 1 n1 ∑ i = 1 n (
Gamma function (13,243 words) [view diff] no match in snippet view article find links to article
non-positive integers. For every positive integer n, Γ ( n ) = ( n1 ) ! . {\displaystyle \Gamma (n)=(n-1)!\,.} Derived by Daniel Bernoulli, for complex numbers
Factorial (8,400 words) [view diff] no match in snippet view article find links to article
factorial: n ! = n × ( n1 ) × ( n − 2 ) × ( n − 3 ) × ⋯ × 3 × 2 × 1 = n × ( n1 ) ! {\displaystyle {\begin{aligned}n!&=n\times (n-1)\times (n-2)\times
Refractive index (8,486 words) [view diff] no match in snippet view article find links to article
normal incidence reduces to: 44  R 0 = | n 1 − n 2 n 1 + n 2 | 2 . {\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\!.} For common glass
Trigonometric functions (8,994 words) [view diff] no match in snippet view article find links to article
tan ⁡ x = ∑ n = 0 ∞ U 2 n + 1 ( 2 n + 1 ) ! x 2 n + 1 = ∑ n = 1 ∞ ( − 1 ) n1 2 2 n ( 2 2 n1 ) B 2 n ( 2 n ) ! x 2 n1 = x + 1 3 x 3 + 2 15 x 5
Summation (4,491 words) [view diff] no match in snippet view article find links to article
progression) ∑ i = 0 n1 ( b + i d ) a i = b ∑ i = 0 n1 a i + d ∑ i = 0 n1 i a i = b ( 1 − a n 1 − a ) + d ( a − n a n + ( n1 ) a n + 1 ( 1 − a ) 2
Recursion (3,664 words) [view diff] exact match in snippet view article find links to article
{\displaystyle G(0)=a} F ( n + 1 ) = f ( F ( n ) ) {\displaystyle F(n+1)=f(F(n))} G ( n + 1 ) = f ( G ( n ) ) {\displaystyle G(n+1)=f(G(n))} where a is an
Median (7,621 words) [view diff] exact match in snippet view article find links to article
\beta } equal to n + 1 {\displaystyle n+1} allows the last expression to be written as F ( v ) n ( 1 − F ( v ) ) n B ( n + 1 , n + 1 ) d F ( v ) {\displaystyle
Gini coefficient (10,528 words) [view diff] exact match in snippet view article find links to article
1 n1 ( n + 1 − 2 ( ∑ i = 1 n ( n + 1 − i ) y i ∑ i = 1 n y i ) ) {\displaystyle G(S)={\frac {1}{n-1}}\left(n+1-2\left({\frac {\sum _{i=1}^{n}(n+1-i)y_{i}}{\sum
2 (3,077 words) [view diff] no match in snippet view article find links to article
In symbols, ∑ n = 0 ∞ 1 2 n = 1 + 1 2 + 1 4 + 1 8 + 1 16 + ⋯ = 2. {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{2^{n}}}=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac
Polygon (4,287 words) [view diff] no match in snippet view article find links to article
y 0 ) , ( x 1 , y 1 ) , … , ( x n1 , y n1 ) {\displaystyle (x_{0},y_{0}),(x_{1},y_{1}),\ldots ,(x_{n-1},y_{n-1})} in order. For convenience in some
Fast Fourier transform (7,331 words) [view diff] no match in snippet view article find links to article
Let x 0 , … , x n1 {\displaystyle x_{0},\ldots ,x_{n-1}} be complex numbers. The DFT is defined by the formula X k = ∑ m = 0 n1 x m e − i 2 π k
Pearson correlation coefficient (8,207 words) [view diff] no match in snippet view article find links to article
( n − 2 ) Γ ( n1 ) ( 1 − ρ 2 ) n1 2 ( 1 − r 2 ) n − 4 2 2 π Γ ⁡ ( n1 2 ) ( 1 − ρ r ) n − 3 2 2 F 1 ( 1 2 , 1 2 ; 1 2 ( 2 n1 ) ; 1 2 ( ρ r
1 (3,551 words) [view diff] no match in snippet view article find links to article
{\displaystyle n} multiplied or divided by 1 remains unchanged ( n × 1 = n / 1 = n {\displaystyle n\times 1=n/1=n} ). This makes it a mathematical unit, and for this
10 (3,204 words) [view diff] exact match in snippet view article find links to article
Retrieved 2022-12-08. Sloane, N. J. A. (ed.). "Sequence A108100 ((2*n-1)^2+(2*n+1)^2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation
Binomial coefficient (10,483 words) [view diff] no match in snippet view article find links to article
formula ( n k ) = n × ( n1 ) × ⋯ × ( n − k + 1 ) k × ( k − 1 ) × ⋯ × 1 , {\displaystyle {\binom {n}{k}}={\frac {n\times (n-1)\times \cdots \times (n-k+1)}{k\times
Sine and cosine (6,000 words) [view diff] no match in snippet view article find links to article
complex analysis, one can find that the infinite series ∑ n = − ∞ ∞ ( − 1 ) n z − n = 1 z − 2 z ∑ n = 1 ∞ ( − 1 ) n n 2 − z 2 {\displaystyle \sum _{n=-\infty
Recursion (computer science) (6,890 words) [view diff] no match in snippet view article
hanoi ⁡ ( n ) = { 1 if  n = 1 2 ⋅ hanoi ⁡ ( n1 ) + 1 if  n > 1 {\displaystyle \operatorname {hanoi} (n)={\begin{cases}1&{\mbox{if }}n=1\\2\cdot \operatorname
Exponential distribution (6,543 words) [view diff] exact match in snippet view article find links to article
n + 1 ∣ x 1 , … , x n ) = n n + 1 ( x ¯ ) n ( n x ¯ + x n + 1 ) n + 1 , {\displaystyle p_{\rm {CNML}}(x_{n+1}\mid x_{1},\ldots ,x_{n})={\frac {n^{n+1}\left({\overline
Natural logarithm (6,072 words) [view diff] exact match in snippet view article find links to article
= n + 1 n {\displaystyle x={\tfrac {n+1}{n}}} for positive integers n, we get: ln ⁡ ( n + 1 n ) = ∑ k = 1 ∞ 1 k ( n + 1 ) k = 1 n + 1 + 1 2 ( n + 1 )
Newton's method (7,140 words) [view diff] exact match in snippet view article find links to article
initial guess, x0. The process is repeated as x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} until a
Student's t-test (6,651 words) [view diff] no match in snippet view article find links to article
Z i 2 n1 ∼ χ n1 2 n1 × ( σ 1 2 m + σ 2 2 n ) {\displaystyle {\frac {\sum _{i=2}^{n}Z_{i}^{2}}{n-1}}\sim {\frac {\chi _{n-1}^{2}}{n-1}}\times
Binomial theorem (6,250 words) [view diff] exact match in snippet view article find links to article
Thus ( x + y ) n + 1 = ∑ k = 0 n + 1 ( n + 1 k ) x n + 1 − k y k , {\displaystyle (x+y)^{n+1}=\sum _{k=0}^{n+1}{\binom {n+1}{k}}x^{n+1-k}y^{k},} which is
Markov chain (13,167 words) [view diff] exact match in snippet view article find links to article
( X t n + 1 = i n + 1 ∣ X t 0 = i 0 , X t 1 = i 1 , … , X t n = i n ) = p i n i n + 1 ( t n + 1 − t n ) {\displaystyle \Pr(X_{t_{n+1}}=i_{n+1}\mid X_{t_{0}}=i_{0}
Sequence (6,094 words) [view diff] no match in snippet view article find links to article
2 = 2 nd element  a 3 = 3 rd element  ⋮ a n1 = ( n1 ) th element a n = n th element a n + 1 = ( n + 1 ) th element ⋮ {\displaystyle
Lens (6,308 words) [view diff] no match in snippet view article find links to article
and image is given by n 2 v + n 1 u = n 2 − n 1 R {\displaystyle {\frac {n_{2}}{v}}+{\frac {n_{1}}{u}}={\frac {n_{2}-n_{1}}{R}}} where R is the radius
Discrete cosine transform (12,046 words) [view diff] no match in snippet view article find links to article
k 2 = ∑ n 1 = 0 N 1 − 1 ( ∑ n 2 = 0 N 2 − 1 x n 1 , n 2 cos ⁡ [ π N 2 ( n 2 + 1 2 ) k 2 ] ) cos ⁡ [ π N 1 ( n 1 + 1 2 ) k 1 ] = ∑ n 1 = 0 N 1 − 1 ∑ n
Fourier transform (21,136 words) [view diff] no match in snippet view article find links to article
\mathbb {Z} ,} whose amplitude and phase are given by the analysis formula: c n = 1 P ∫ − P / 2 P / 2 f ( x ) e − i 2 π n P x d x . {\displaystyle c_{n}={\tfrac
Riemann zeta function (10,186 words) [view diff] no match in snippet view article find links to article
complex variable defined as ζ ( s ) = ∑ n = 1 ∞ 1 n s = 1 1 s + 1 2 s + 1 3 s + ⋯ {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac
Refraction (2,570 words) [view diff] no match in snippet view article find links to article
the refractive indices n 2 n 1 {\displaystyle {\frac {n_{2}}{n_{1}}}} of the two media: sin ⁡ θ 1 sin ⁡ θ 2 = v 1 v 2 = n 2 n 1 {\displaystyle {\frac {\sin
Percentile (2,587 words) [view diff] exact match in snippet view article find links to article
than 1 N + 1 {\displaystyle {\frac {1}{N+1}}} is also excluded and would cause an error.) x = f ( p , N ) = { 1 ,  p ∈ [ 0 , 1 N + 1 ] p ( N + 1 ) ,  p
M1 motorway (4,242 words) [view diff] no match in snippet view article find links to article
53°06′05″N 1°19′26″W / 53.1013°N 1.3240°W / 53.1013; -1.3240 (M1, Junction 28) Tibshelf 138.3 222.5 Tibshelf services 53°08′19″N 1°19′51″W / 53.1385°N 1
Cross product (11,439 words) [view diff] no match in snippet view article find links to article
( 1 , n1 ) {\displaystyle (1,n-1)} -tensor, which takes as input n1 {\displaystyle n-1} vectors, and gives as output 1 vector – an ( n1 ) {\displaystyle
Moving average (2,876 words) [view diff] exact match in snippet view article find links to article
1 {\displaystyle {\textit {CA}}_{n+1}} results in CA n + 1 = x n + 1 + n ⋅ CA n n + 1 = x n + 1 + ( n + 1 − 1 ) ⋅ CA n n + 1 = ( n + 1 ) ⋅ CA n + x n
Triangular number (3,159 words) [view diff] exact match in snippet view article find links to article
= n ( n + 1 ) 2 = n 2 + n 2 = ( n + 1 2 ) , {\displaystyle T_{n}=\sum _{k=1}^{n}k=1+2+3+\dotsb +n={\frac {n(n+1)}{2}}={\frac {n^{2}+n}{2}}={n+1 \choose
Dirac delta function (13,810 words) [view diff] no match in snippet view article find links to article
decomposition is: δ ( x ) = { ( n1 ) ! ( 2 π i ) n ∫ S n1 ( x ⋅ ξ ) − n d ω ξ n  even 1 2 ( 2 π i ) n1 ∫ S n1 δ ( n1 ) ( x ⋅ ξ ) d ω ξ n  odd
Moving average (2,876 words) [view diff] exact match in snippet view article find links to article
1 {\displaystyle {\textit {CA}}_{n+1}} results in CA n + 1 = x n + 1 + n ⋅ CA n n + 1 = x n + 1 + ( n + 1 − 1 ) ⋅ CA n n + 1 = ( n + 1 ) ⋅ CA n + x n
Finance (5,997 words) [view diff] no match in snippet view article find links to article
∑ t = 1 n F C F F t ( 1 + W A C C t ) t + [ F C F F n + 1 ( W A C C n + 1 − g n + 1 ) ] ( 1 + W A C C n ) n {\displaystyle \sum _{t=1}^{n}{\frac
3 (3,091 words) [view diff] no match in snippet view article find links to article
known number n {\displaystyle n} such that n {\displaystyle n} ! − 1 and n {\displaystyle n} ! + 1 are prime, as well as the only prime number p {\displaystyle
Geometric series (11,779 words) [view diff] no match in snippet view article find links to article
n = 1 ∞ ( 1 − w 2 n ) ( 1 + w 2 n1 ) 2 {\displaystyle \vartheta _{00}(w)=\prod _{n=1}^{\infty }(1-w^{2n})(1+w^{2n-1})^{2}} ψ H ( w ) = ∏ n = 1
Ideal gas law (4,482 words) [view diff] no match in snippet view article find links to article
5 N T = C 5 or N 1 T 1 = N 2 T 2 {\displaystyle NT=C_{5}\quad {\text{or}}\quad N_{1}T_{1}=N_{2}T_{2}} Equation 6 P N = C 6 or P 1 N 1 = P 2 N 2 {\displaystyle
Continuous uniform distribution (4,150 words) [view diff] exact match in snippet view article find links to article
b − a = b n + 1 − a n + 1 ( n + 1 ) ( b − a ) . {\displaystyle E(X^{n})=\int _{a}^{b}x^{n}{\frac {dx}{b-a}}={\frac {b^{n+1}-a^{n+1}}{(n+1)(b-a)}}.} The
Series (mathematics) (9,676 words) [view diff] exact match in snippet view article
alternating series ∑ n = 1 ∞ ( − 1 ) n + 1 n = 1 − 1 2 + 1 3 − 1 4 + 1 5 − ⋯ , {\displaystyle \sum \limits _{n=1}^{\infty }{(-1)^{n+1} \over n}=1-{1 \over 2}+{1
Uncertainty principle (19,094 words) [view diff] exact match in snippet view article find links to article
n + 1 | n + 1 ⟩ {\displaystyle a^{\dagger }|n\rangle ={\sqrt {n+1}}|n+1\rangle } a | n ⟩ = n | n1 ⟩ , {\displaystyle a|n\rangle ={\sqrt {n}}|n-1\rangle
1000 (number) (25,170 words) [view diff] no match in snippet view article
3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n >
Determinant (14,070 words) [view diff] no match in snippet view article find links to article
M_{i,j}} is defined to be the determinant of the ( n1 ) × ( n1 ) {\displaystyle (n-1)\times (n-1)} -matrix that results from A {\displaystyle A} by
Entropy (information theory) (9,695 words) [view diff] no match in snippet view article
increase with the number of outcomes i.e. H n ( 1 n , … , 1 n ⏟ n ) < H n + 1 ( 1 n + 1 , … , 1 n + 1n + 1 ) . {\displaystyle \mathrm {H} _{n}{\bigg
Simplex (7,560 words) [view diff] exact match in snippet view article find links to article
x / n + 1 {\displaystyle dx/{\sqrt {n+1}}} of the increment, ( d x / ( n + 1 ) , … , d x / ( n + 1 ) ) {\displaystyle (dx/(n+1),\ldots ,dx/(n+1))} ,
Quicksort (9,995 words) [view diff] no match in snippet view article find links to article
n1 ) C ( n1 ) = n ( n1 ) − ( n1 ) ( n − 2 ) + 2 C ( n1 ) {\displaystyle nC(n)-(n-1)C(n-1)=n(n-1)-(n-1)(n-2)+2C(n-1)} n C ( n ) = ( n +
Recurrence relation (4,158 words) [view diff] no match in snippet view article find links to article
= ( n1 k − 1 ) + ( n1 k ) , {\displaystyle {\binom {n}{k}}={\binom {n-1}{k-1}}+{\binom {n-1}{k}},} with the base cases ( n 0 ) = ( n n ) = 1 {\displaystyle
Mathematical induction (6,840 words) [view diff] exact match in snippet view article find links to article
among all n + 1 {\displaystyle n+1} horses. The base case n = 1 {\displaystyle n=1} is trivial, and the induction step is correct in all cases n > 1 {\displaystyle
Mann–Whitney U test (5,778 words) [view diff] no match in snippet view article find links to article
of: U 1 = n 1 n 2 + n 1 ( n 1 + 1 ) 2 − R 1 , U 2 = n 1 n 2 + n 2 ( n 2 + 1 ) 2 − R 2 {\displaystyle U_{1}=n_{1}n_{2}+{\tfrac {n_{1}(n_{1}+1)}{2}}-R_{1}
Hash function (7,840 words) [view diff] no match in snippet view article find links to article
key K = ( k n1 . . . k 1 k 0 ) 2 {\displaystyle K=(k_{n-1}...k_{1}k_{0})_{2}} can be regarded as the polynomial K ( x ) = k n1 x n1 + . . . + k
Atomic orbital (10,600 words) [view diff] no match in snippet view article find links to article
n , 1 , + 1 real = R n , 1 3 4 π ⋅ x r ψ n , 1 , − 1 real = R n , 1 3 4 π ⋅ y r {\displaystyle {\begin{aligned}\psi _{n,1,+1}^{\text{real}}=&R_{n,1}{\sqrt
Fourier series (10,850 words) [view diff] exact match in snippet view article find links to article
) = 2 ∑ n = 1 ∞ ( − 1 ) n + 1 n sin ⁡ ( n x ) sinh ⁡ ( n y ) sinh ⁡ ( n π ) . {\displaystyle T(x,y)=2\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}\sin(nx){\sinh(ny)
Expected value (7,633 words) [view diff] exact match in snippet view article find links to article
= X 1 {\displaystyle Y_{0}=X_{1}} and Y n = X n + 1 − X n {\displaystyle Y_{n}=X_{n+1}-X_{n}} for n1 , {\displaystyle n\geq 1,} where X n {\displaystyle
Floor and ceiling functions (5,868 words) [view diff] no match in snippet view article find links to article
= 1 n1 ⌈ k m n ⌉ = 1 2 ( m + 1 ) ( n1 ) , {\displaystyle \sum _{k=1}^{n-1}\left\lceil {\frac {km}{n}}\right\rceil ={\tfrac {1}{2}}(m+1)(n-1),} ∑
Mandelbrot set (7,513 words) [view diff] exact match in snippet view article find links to article
those of the real logistic family, x n + 1 = r x n ( 1 − x n ) , r ∈ [ 1 , 4 ] . {\displaystyle x_{n+1}=rx_{n}(1-x_{n}),\quad r\in [1,4].} The correspondence
Big O notation (8,017 words) [view diff] no match in snippet view article find links to article
following are true for n → ∞ {\displaystyle n\to \infty } : ( n + 1 ) 2 = n 2 + O ( n ) , ( n + O ( n 1 / 2 ) ) ⋅ ( n + O ( log ⁡ n ) ) 2 = n 3 + O ( n 5 / 2
Exponentiation (13,585 words) [view diff] no match in snippet view article find links to article
sides by b n {\displaystyle b^{n}} gives b 0 = b n / b n = 1 {\displaystyle b^{0}=b^{n}/b^{n}=1} . The fact that b 1 = b {\displaystyle b^{1}=b} can similarly
Discrete Fourier transform (10,475 words) [view diff] no match in snippet view article find links to article
⋅ 1 ⋯ ω N 0 ⋅ ( N1 ) ω N 1 ⋅ 0 ω N 1 ⋅ 1 ⋯ ω N 1 ⋅ ( N1 ) ⋮ ⋮ ⋱ ⋮ ω N ( N1 ) ⋅ 0 ω N ( N1 ) ⋅ 1 ⋯ ω N ( N1 ) ⋅ ( N1 ) ] {\displaystyle
Lp space (12,891 words) [view diff] exact match in snippet view article find links to article
t n + 1 = 0 {\displaystyle t_{n+1}=0} and ( t n + 1 < f ≤ t n ) = ∅ {\displaystyle (t_{n+1}<f\leq t_{n})=\varnothing } so that f n = 1 r n f 1 ( t n +
Kurtosis (5,201 words) [view diff] no match in snippet view article find links to article
n + 1 ) m 4 − 3 ( n1 ) m 2 2 ] ( n1 ) ( n − 2 ) ( n − 3 ) ( n1 ) 2 n 2 m 2 2 = n1 ( n − 2 ) ( n − 3 ) [ ( n + 1 ) m 4 m 2 2 − 3 ( n1 )
Binary search algorithm (9,602 words) [view diff] no match in snippet view article find links to article
T(n)} : T ( n ) = 1 + ( n + 1 ) ⌊ log 2 ⁡ ( n + 1 ) ⌋ − 2 ⌊ log 2 ⁡ ( n + 1 ) ⌋ + 1 + 2 n = ⌊ log 2 ⁡ ( n ) ⌋ + 1 − ( 2 ⌊ log 2 ⁡ ( n ) ⌋ + 1 − ⌊ log 2
Invertible matrix (7,017 words) [view diff] no match in snippet view article find links to article
the linear Diophantine equation s + ∑ l = 1 n1 l k l = n1. {\displaystyle s+\sum _{l=1}^{n-1}lk_{l}=n-1.} The formula can be rewritten in terms of
Hyperbolic functions (4,822 words) [view diff] no match in snippet view article find links to article
n = 1 ∞ 2 2 n ( 2 2 n1 ) B 2 n x 2 n1 ( 2 n ) ! , | x | < π 2 coth ⁡ x = x − 1 + x 3 − x 3 45 + 2 x 5 945 + ⋯ = ∑ n = 0 ∞ 2 2 n B 2 n x 2 n1
20 (number) (2,562 words) [view diff] exact match in snippet view article
form ( 2 P n P n + 1 , P n + 1 2 − P n 2 , P n + 1 2 + P n 2 = P 2 n + 1 ) {\displaystyle \left(2P_{n}P_{n+1},P_{n+1}^{2}-P_{n}^{2},P_{n+1}^{2}+P_{n}^{2}=P_{2n+1}\right)}
N-sphere (5,824 words) [view diff] case mismatch in snippet view article find links to article
s_{n-2}s_{n-1})(s_{n-1}|J_{n-1}|)\\&\qquad {}+(-1)^{n+n}(rs_{1}\dotsm s_{n-2}c_{n-1})(c_{n-1}|J_{n-1}|)\\&=(rs_{1}\dotsm s_{n-2}|J_{n-1}|(s_{n-1}^{2}+c_{n-1
Diffusion (8,402 words) [view diff] no match in snippet view article find links to article
expression: C 1 − C 2 = − n 2 n 1 n 2 D 12 { ∇ ( n 1 n ) + n 1 n 2 ( m 2 − m 1 ) P n ( m 1 n 1 + m 2 n 2 ) ∇ P − m 1 n 1 m 2 n 2 P ( m 1 n 1 + m 2 n 2 ) ( F 1 −
Bézier curve (6,966 words) [view diff] no match in snippet view article find links to article
n + 1 b i , n + 1 ( t ) P i + ∑ i = 0 n i + 1 n + 1 b i + 1 , n + 1 ( t ) P i = ∑ i = 0 n + 1 ( i n + 1 P i − 1 + n + 1 − i n + 1 P i ) b i , n + 1 (
Central limit theorem (8,929 words) [view diff] no match in snippet view article find links to article
since the asymptotic normality fails for X n = Y n − Y n1 {\textstyle X_{n}=Y_{n}-Y_{n-1}} where Y n {\textstyle Y_{n}} are another stationary sequence
Effect size (8,124 words) [view diff] no match in snippet view article find links to article
n 1 + n 2 n 1 n 2 + ( g ∗ ) 2 2 ( n 1 + n 2 ) . {\displaystyle {\hat {\sigma }}^{2}(g^{*})={\frac {n_{1}+n_{2}}{n_{1}n_{2}}}+{\frac {(g^{*})^{2}}{2(n_{1}+n_{2})}}
Bessel function (10,584 words) [view diff] exact match in snippet view article find links to article
n1 ( x ) y n ( x ) = ( − 1 ) n + 1 j − n1 ( x ) {\displaystyle {\begin{aligned}j_{n}(x)&=(-1)^{n}y_{-n-1}(x)\\y_{n}(x)&=(-1)^{n+1}j_{-n-1}(x)\end{aligned}}}
Histogram (3,135 words) [view diff] no match in snippet view article find links to article
cross validation: a r g m i n h J ^ ( h ) = a r g m i n h ( 2 ( n1 ) h − n + 1 n 2 ( n1 ) h ∑ k N k 2 ) {\displaystyle {\underset {h}{\operatorname
North Sea (11,989 words) [view diff] no match in snippet view article find links to article
Walde (Walde Lighthouse, in France, 50°59'37"N, 1°54'53"E) and Leathercoat Point (England, 51°10'01.4"N 1°24'07.8"). northeast of Dover. On the Northwest
Snell's law (3,817 words) [view diff] no match in snippet view article find links to article
is equal to the ratio of the refractive indices ( n 2 n 1 {\displaystyle {\tfrac {n_{2}}{n_{1}}}} ) of the two media, or equivalently, to the ratio of
Oxfordshire (2,326 words) [view diff] no match in snippet view article find links to article
and the D’Arcy Dalton Way. Northernmost point: 52°10′6.58″N 1°19′54.92″W / 52.1684944°N 1.3319222°W / 52.1684944; -1.3319222, near Claydon Hay Farm
Birthday problem (6,897 words) [view diff] no match in snippet view article find links to article
p ¯ ( n ) ≈ 1 ⋅ e − 1 / 365 ⋅ e − 2 / 365 ⋯ e − ( n1 ) / 365 = e − ( 1 + 2 + ⋯ + ( n1 ) ) / 365 = e − n ( n1 ) / 2 365 = e − n ( n1 ) 730
Support vector machine (8,802 words) [view diff] exact match in snippet view article find links to article
y n + 1 {\displaystyle y_{n+1}} given X n + 1 {\displaystyle X_{n+1}} . To do so one forms a hypothesis, f {\displaystyle f} , such that f ( X n + 1 )
Graham's number (3,272 words) [view diff] no match in snippet view article find links to article
3 , n = 1 3 ↑ g n1 3 , n ≥ 2 , n ∈ N {\displaystyle g_{n}=\left\{{\begin{matrix}3\uparrow \uparrow \uparrow \uparrow 3,&n=1\\3\uparrow ^{g_{n-1}}3,&n\geq
Euclidean vector (9,030 words) [view diff] no match in snippet view article find links to article
\end{aligned}}} Distributing the dot-multiplication gives u = p e 1 ⋅ n 1 + q e 2 ⋅ n 1 + r e 3 ⋅ n 1 , v = p e 1 ⋅ n 2 + q e 2 ⋅ n 2 + r e 3 ⋅ n 2 , w = p e 1 ⋅
Spiral (4,431 words) [view diff] no match in snippet view article find links to article
gets A = 1 2 ∫ φ 1 φ 2 a 2 φ 2 n d φ = a 2 2 ( 2 n + 1 ) ( φ 2 2 n + 1 − φ 1 2 n + 1 )   , if n ≠ − 1 2 , {\displaystyle A={\frac {1}{2}}\int _{\varphi
Antiderivative (3,294 words) [view diff] exact match in snippet view article find links to article
x n + 1 n + 1 + c {\displaystyle F(x)={\tfrac {x^{n+1}}{n+1}}+c} if n ≠ −1, and F ( x ) = log ⁡ | x | + c {\displaystyle F(x)=\log |x|+c} if n = −1. In
Power series (3,366 words) [view diff] no match in snippet view article find links to article
n = 1 ∞ a n n ( x − c ) n1 = ∑ n = 0 ∞ a n + 1 ( n + 1 ) ( x − c ) n , ∫ f ( x ) d x = ∑ n = 0 ∞ a n ( x − c ) n + 1 n + 1 + k = ∑ n = 1 ∞ a n1
Logistic regression (20,426 words) [view diff] exact match in snippet view article find links to article
explanatory variables (including x0) and N + 1 {\displaystyle N+1} categories, we will need N + 1 {\displaystyle N+1} separate probabilities, one for each
Logistic regression (20,426 words) [view diff] exact match in snippet view article find links to article
explanatory variables (including x0) and N + 1 {\displaystyle N+1} categories, we will need N + 1 {\displaystyle N+1} separate probabilities, one for each
Tuple (2,178 words) [view diff] no match in snippet view article find links to article
pairs; indeed, a n-tuple can be identified with the ordered pair of its (n1) first elements and its nth element. Tuples are usually written by listing
Chi-squared distribution (6,364 words) [view diff] no match in snippet view article find links to article
logarithm of the characteristic function: κ n = 2 n1 ( n1 ) ! k {\displaystyle \kappa _{n}=2^{n-1}(n-1)!\,k} The chi-squared distribution exhibits strong
Power series (3,366 words) [view diff] no match in snippet view article find links to article
n = 1 ∞ a n n ( x − c ) n1 = ∑ n = 0 ∞ a n + 1 ( n + 1 ) ( x − c ) n , ∫ f ( x ) d x = ∑ n = 0 ∞ a n ( x − c ) n + 1 n + 1 + k = ∑ n = 1 ∞ a n1
Continued fraction (9,525 words) [view diff] no match in snippet view article find links to article
h n1 − k n1   h n = ( − 1 ) n   , {\displaystyle k_{n}\ h_{n-1}-k_{n-1}\ h_{n}=(-1)^{n}\ ,} or equivalently h n   k n   − h n1   k n1   =
Limit (mathematics) (5,698 words) [view diff] no match in snippet view article
the Basel problem, where a n = 1 / n 2 {\displaystyle a_{n}=1/n^{2}} . Then ∑ n = 1 ∞ 1 n 2 = π 2 6 . {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac
Compressor (7,010 words) [view diff] no match in snippet view article find links to article
− T 1 ) n1 = n R T 1 n1 [ ( P 2 P 1 ) ( n1 ) / n1 ] {\displaystyle W_{comp,in}={\frac {nR(T_{2}-T_{1})}{n-1}}={\frac {nRT_{1}}{n-1}}\left[\left({\frac
Stirling's approximation (4,688 words) [view diff] no match in snippet view article find links to article
n = 1 N1 B 2 n 2 n ( 2 n1 ) z 2 n1 , {\displaystyle \ln \Gamma (z)\sim z\ln z-z+{\tfrac {1}{2}}\ln {\frac {2\pi }{z}}+\sum _{n=1}^{N-1}{\frac
Isambard Kingdom Brunel (7,788 words) [view diff] no match in snippet view article find links to article
-2.399764 (Charfield station) ST7233192265 Charlbury 51°52′19″N 1°29′24″W / 51.872°N 1.49°W / 51.872; -1.49 (Charlbury station) SP3510819441 Chippenham
Factorization (7,734 words) [view diff] no match in snippet view article find links to article
E n1 + E n − 2 F + E n − 3 F 2 + ⋯ + E F n − 2 + F n1 ) {\displaystyle E^{n}-F^{n}=(E-F)(E^{n-1}+E^{n-2}F+E^{n-3}F^{2}+\cdots +EF^{n-2}+F^{n-1})}
Arithmetic progression (2,003 words) [view diff] no match in snippet view article find links to article
n {\displaystyle a_{n}} ) is given by: a n = a 1 + ( n1 ) d {\displaystyle a_{n}=a_{1}+(n-1)d} A finite portion of an arithmetic progression is called
Decimal (5,010 words) [view diff] no match in snippet view article find links to article
[x]n1. This way one has [x]n = [x]0.d1d2...dn−1dn, and the difference of [x]n1 and [x]n amounts to | [ x ] n − [ x ] n1 | = d n ⋅ 10 − n < 10 − n +
Mean squared error (3,827 words) [view diff] no match in snippet view article find links to article
1 2 − σ 2 ) 2 ] = E ⁡ [ ( n1 ) 2 a 2 S n1 4 − 2 ( n1 a S n1 2 ) σ 2 + σ 4 ] = ( n1 ) 2 a 2 E ⁡ [ S n1 4 ] − 2 ( n1 a ) E ⁡ [ S n
Diophantine equation (4,788 words) [view diff] no match in snippet view article find links to article
x n1 = r n1 + t n1 ( x 1 − r 1 ) . {\displaystyle {\begin{aligned}x_{2}&=r_{2}+t_{2}(x_{1}-r_{1})\\&\;\;\vdots \\x_{n-1}&=r_{n-1}+t_{n-1}(x_{1}-r_{1})
Euler's totient function (6,440 words) [view diff] no match in snippet view article find links to article
gcd(9, 9) = 9. Therefore, φ(9) = 6. As another example, φ(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1
Wilcoxon signed-rank test (7,161 words) [view diff] exact match in snippet view article find links to article
+ n = n ( n + 1 ) / 2 {\displaystyle 1+2+\dots +n=n(n+1)/2} , these three statistics are related by: T + = n ( n + 1 ) 2 − T − = n ( n + 1 ) 4 + T 2
Queueing theory (4,854 words) [view diff] exact match in snippet view article find links to article
_{1}+\mu _{1})P_{1}} λ n1 P n1 + μ n + 1 P n + 1 = ( λ n + μ n ) P n {\displaystyle \lambda _{n-1}P_{n-1}+\mu _{n+1}P_{n+1}=(\lambda _{n}+\mu _{n})P_{n}}
Natural number (5,462 words) [view diff] no match in snippet view article find links to article
3 = 2 ∪ {2} = {0, 1, 2} = {{ }, {{ }}, {{ }, {{ }}}}, n = n1 ∪ {n1} = {0, 1, ..., n1} = {{ }, {{ }}, ..., {{ }, {{ }}, ...}}, etc. It can be checked
Perfect number (4,913 words) [view diff] no match in snippet view article find links to article
perfect number is of the form 2 n1 ( 2 n1 ) {\displaystyle 2^{n-1}(2^{n}-1)} where 2 n1 {\displaystyle 2^{n}-1} is prime. He seems to be unaware
Multivariate normal distribution (9,474 words) [view diff] no match in snippet view article find links to article
1 n1 ∑ i = 1 n ( x i − x ¯ ) ( x i − x ¯ ) T = 1 n1 [ X ′ ( I − 1 n ⋅ J ) X ] {\displaystyle {\widehat {\boldsymbol {\Sigma }}}={\frac {1}{n-1}}\sum
M62 motorway (4,828 words) [view diff] no match in snippet view article find links to article
of M62) 53°39′36″N 1°51′41″W / 53.6601°N 1.8613°W / 53.6601; -1.8613 (Junction 23 of M62) 53°40′18″N 1°50′00″W / 53.6717°N 1.8332°W / 53.6717;
Tree (graph theory) (3,282 words) [view diff] no match in snippet view article
also equivalent to any of the following conditions: G is connected and has n1 edges. G is connected, and every subgraph of G includes at least one vertex
Quantum logic gate (10,122 words) [view diff] no match in snippet view article find links to article
n1 ( H | 0 ⟩ ) = 1 2 n [ 1 1 ⋮ 1 ] = 1 2 n ( | 0 ⟩ + | 1 ⟩ + ⋯ + | 2 n1 ⟩ ) = 1 2 n ∑ i = 0 2 n1 | i ⟩ {\displaystyle \bigotimes _{0}^{n-1}(H|0\rangle
Rotation matrix (15,019 words) [view diff] no match in snippet view article find links to article
matrix will have (n1) + (n − 2) + ⋯ + 2 + 1, or ∑ k = 1 n1 k = 1 2 n ( n1 ) {\displaystyle \sum _{k=1}^{n-1}k={\frac {1}{2}}n(n-1)} entries below
Dynamic programming (9,215 words) [view diff] no match in snippet view article find links to article
obtained in state y at the last time n. The values Vi at earlier times i = n −1, n − 2, ..., 2, 1 can be found by working backwards, using a recursive relationship
Stainless steel (10,037 words) [view diff] no match in snippet view article find links to article
+ ∑ n = 1 N OC ( 1 + i ) n + ∑ n = 1 N LP ( 1 + i ) n + ∑ n = 1 N RC ( 1 + i ) n {\displaystyle {\text{LCC}}={\text{AC}}+{\text{IC}}+\sum _{n=1}^{N}{\frac
Harmonic series (mathematics) (6,143 words) [view diff] no match in snippet view article
positive unit fractions: ∑ n = 1 ∞ 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ . {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac
Avogadro constant (2,229 words) [view diff] no match in snippet view article find links to article
Avogadro constant is the reciprocal of amount of substance, N1 {\displaystyle {\mathsf {N}}^{-1}} . The Avogadro number, sometimes denoted N0, is the numeric
N1 (rocket) (7,881 words) [view diff] no match in snippet view article
N-1: For the Moon and Mars A Guide to the Soviet Superbooster. ARA Press; First edition. ISBN 9780989991407. Wikimedia Commons has media related to N-1
Bias of an estimator (5,350 words) [view diff] no match in snippet view article find links to article
[nS^{2}]=(n-1)\sigma ^{2}{\text{ and }}\operatorname {Var} (nS^{2})=2(n-1)\sigma ^{4}.} and so MSE = ( c ( n1 ) − 1 ) 2 σ 4 + 2 c 2 ( n1 ) σ 4 {\displaystyle
Matrix multiplication (6,025 words) [view diff] no match in snippet view article find links to article
C = ( a 11 b 11 + ⋯ + a 1 n b n 1 a 11 b 12 + ⋯ + a 1 n b n 2 ⋯ a 11 b 1 p + ⋯ + a 1 n b n p a 21 b 11 + ⋯ + a 2 n b n 1 a 21 b 12 + ⋯ + a 2 n b n 2 ⋯
M6 motorway (3,736 words) [view diff] no match in snippet view article find links to article
extension: 2008 Major junctions South end Catthorpe 52°24′01″N 1°10′31″W / 52.4004°N 1.1752°W / 52.4004; -1.1752 (M6, southern terminus) Major intersections
Real number (7,562 words) [view diff] no match in snippet view article find links to article
that D n1 + a n / 10 n ≤ a , {\displaystyle D_{n-1}+a_{n}/10^{n}\leq a,} and one sets D n = D n1 + a n / 10 n . {\displaystyle D_{n}=D_{n-1}+a_{n}/10^{n}
Logarithm (11,492 words) [view diff] exact match in snippet view article find links to article
integers. Putting z = n + 1 n {\displaystyle \textstyle z={\frac {n+1}{n}}} in the above series, it follows that: ln ⁡ ( n + 1 ) = ln ⁡ ( n ) + 2 ∑ k
Geometric mean (4,878 words) [view diff] exact match in snippet view article find links to article
are defined: a n + 1 = a n + h n 2 , a 0 = x {\displaystyle a_{n+1}={\frac {a_{n}+h_{n}}{2}},\quad a_{0}=x} and h n + 1 = 2 1 a n + 1 h n , h 0 = y {\displaystyle
Collatz conjecture (7,014 words) [view diff] no match in snippet view article find links to article
the function f as follows: f ( n ) = { n / 2 if  n ≡ 0 ( mod 2 ) , 3 n + 1 if  n1 ( mod 2 ) . {\displaystyle f(n)={\begin{cases}n/2&{\text{if }}n\equiv
Laplace transform (8,154 words) [view diff] no match in snippet view article find links to article
− s n1 f ( 0 − ) − ⋯ − f ( n1 ) ( 0 − ) , {\displaystyle {\mathcal {L}}\left\{f^{(n)}(t)\right\}=s^{n}\cdot {\mathcal {L}}\{f(t)\}-s^{n-1}f(0^{-})-\cdots
Capacitance (4,182 words) [view diff] no match in snippet view article find links to article
N = 1 {\displaystyle \Delta N=1} and Δ Q = e . {\displaystyle \Delta Q=e.} The "quantum capacitance" of the device is then C Q ( N ) = e 2 μ ( N + 1 )
Europe 1 (2,399 words) [view diff] no match in snippet view article find links to article
Europe 1, (Europe un) formerly known as Europe n° 1, is a privately owned radio station created in 1955. It was owned and operated by Lagardère Active
Newton (unit) (958 words) [view diff] no match in snippet view article
kilogram-force, kilopond pound-force poundal 1 N1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl 1 dyn = 10–5 N ≡ 1 g⋅cm/s2 ≈ 1.0197×10−6 kp ≈ 2.2481×10−6 lbf
Square number (2,534 words) [view diff] no match in snippet view article find links to article
= (n1)2 + (n1) + n = (n1)2 + (2n − 1). Alternatively, the nth square number can be calculated from the previous two by doubling the (n − 1)th
Capacitor (14,954 words) [view diff] exact match in snippet view article find links to article
1 n + 1 ) (volts) B 1..n = A n ( 1 − 1 n + 1 ) A − B = 0 {\displaystyle {\begin{aligned}{\text{(volts)}}A_{\mathrm {eq} }&=A\left(1-{\frac {1}{n+1
Combination (3,936 words) [view diff] no match in snippet view article find links to article
n1 k − 1 ) + ( n1 k ) , {\displaystyle {\binom {n}{k}}={\binom {n-1}{k-1}}+{\binom {n-1}{k}},} for 0 < k < n, which follows from (1 + X)n = (1 +
Skewness (3,957 words) [view diff] exact match in snippet view article find links to article
var ⁡ ( G 1 ) = 6 n ( n1 ) ( n − 2 ) ( n + 1 ) ( n + 3 ) . {\displaystyle \operatorname {var} (G_{1})={\frac {6n(n-1)}{(n-2)(n+1)(n+3)}}.} In normal
Time complexity (4,846 words) [view diff] no match in snippet view article find links to article
{\tilde {O}}(n)} . Quasilinear time algorithms are also O ( n 1 + ε ) {\displaystyle O(n^{1+\varepsilon })} for every constant ε > 0 {\displaystyle \varepsilon
Integration by parts (6,846 words) [view diff] no match in snippet view article find links to article
product for π {\displaystyle \pi } π 2 = ∏ n = 1 ∞ 4 n 2 4 n 2 − 1 = ∏ n = 1 ∞ ( 2 n 2 n1 ⋅ 2 n 2 n + 1 ) = ( 2 1 ⋅ 2 3 ) ⋅ ( 4 3 ⋅ 4 5 ) ⋅ ( 6 5 ⋅
Riemann hypothesis (16,487 words) [view diff] no match in snippet view article find links to article
s ) = ∑ n = 1 ∞ ( − 1 ) n + 1 n s = 1 1 s − 1 2 s + 1 3 s − ⋯ , {\displaystyle \left(1-{\frac {2}{2^{s}}}\right)\zeta (s)=\eta (s)=\sum _{n=1}^{\infty
Kruskal–Wallis test (2,415 words) [view diff] exact match in snippet view article find links to article
exactly ( N1 ) N ( N + 1 ) / 12 {\displaystyle (N-1)N(N+1)/12} and r ¯ = N + 1 2 {\displaystyle {\bar {r}}={\tfrac {N+1}{2}}} . Thus H = 12 N ( N + 1 ) ∑
Focal length (2,340 words) [view diff] no match in snippet view article find links to article
( n1 ) ( 1 R 1 − 1 R 2 + ( n1 ) d n R 1 R 2 ) , {\displaystyle {\frac {1}{f}}=(n-1)\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}+{\frac {(n-1
Shetland (13,102 words) [view diff] no match in snippet view article find links to article
Brindister: 60°06′52″N 1°12′57″W / 60.114475°N 1.215874°W / 60.114475; -1.215874 Scord: 60°08′32″N 1°15′42″W / 60.142287°N 1.261629°W / 60.142287;
Analysis of algorithms (3,680 words) [view diff] no match in snippet view article find links to article
3 T 5 + 4 T 5 + ⋯ + ( n1 ) T 5 + n T 5 + ( n + 1 ) T 5 =   T 5 + 2 T 5 + 3 T 5 + 4 T 5 + ⋯ + ( n1 ) T 5 + n T 5 + ( n + 1 ) T 5 − T 5 {\displaystyle
Bernoulli number (13,189 words) [view diff] exact match in snippet view article find links to article
for n1 B n = n 2 n + 1 − 2 ∑ k = 0 n1 ( − 2 ) − k W n1 , k . {\displaystyle B_{n}={\frac {n}{2^{n+1}-2}}\sum _{k=0}^{n-1}(-2)^{-k}\,W_{n-1,k}
Elliptic curve (8,223 words) [view diff] no match in snippet view article find links to article
= exp ⁡ ( ∑ n = 1 ∞ ( 1 − α n − α ¯ n + q n ) T n n ) = exp ⁡ ( ∑ n = 1 ∞ T n n − ∑ n = 1 ∞ α n T n n − ∑ n = 1 ∞ α ¯ n T n n + ∑ n = 1 ∞ q n T n n )
Convolution (8,308 words) [view diff] no match in snippet view article find links to article
∗ g N ) [ n ] ≡ ∑ m = 0 N1 ( ∑ k = − ∞ ∞ f [ m + k N ] ) g N [ n − m ] . {\displaystyle (f*g_{N})[n]\equiv \sum _{m=0}^{N-1}\left(\sum _{k=-\infty }^{\infty
Degrees of freedom (statistics) (4,493 words) [view diff] no match in snippet view article
steps (one, namely, the sample mean) and is therefore equal to N1 {\textstyle N-1} . Mathematically, degrees of freedom is the number of dimensions
Euler's formula (3,641 words) [view diff] no match in snippet view article find links to article
x ) = Re ⁡ ( e i ( n1 ) x ⋅ e i x ) = Re ⁡ ( e i ( n1 ) x ⋅ ( e i x + e − i x ⏟ 2 cos ⁡ x − e − i x ) ) = Re ⁡ ( e i ( n1 ) x ⋅ 2 cos ⁡ x − e
Mersenne prime (6,327 words) [view diff] no match in snippet view article find links to article
for which n the number (1 + i)n1 is a Gaussian prime which will then be called a Gaussian Mersenne prime. (1 + i)n1 is a Gaussian prime for the following
Russian roulette (2,914 words) [view diff] no match in snippet view article find links to article
{\displaystyle k} 's all-game loss probability is ( n1 n ) k ⋅ 1 n {\displaystyle ({\tfrac {n-1}{n}})^{k}\cdot {\tfrac {1}{n}}} . The probability of
Benford's law (7,247 words) [view diff] no match in snippet view article find links to article
encountered as the n-th (n > 1) digit is ∑ k = 10 n − 2 10 n1 − 1 log 10 ⁡ ( 1 + 1 10 k + d ) . {\displaystyle \sum _{k=10^{n-2}}^{10^{n-1}-1}\log _{10}\left(1+{\frac
Coefficient of variation (4,018 words) [view diff] no match in snippet view article find links to article
1 / 2 Γ ( n1 2 ) e − n 2 ( σ μ ) 2 c v 2 1 + c v 2 c v n − 2 ( 1 + c v 2 ) n / 2 ∑ ∑ ′ i = 0 n1 ⁡ ( n1 ) ! Γ ( n − i 2 ) ( n1 − i ) ! i
Catalan number (5,838 words) [view diff] exact match in snippet view article find links to article
therefore: ( n1 + n + 1 n1 ) = ( 2 n n1 ) = ( 2 n n + 1 ) {\displaystyle {n-1+n+1 \choose n-1}={2n \choose n-1}={2n \choose n+1}} and the number
Bootstrapping (statistics) (8,256 words) [view diff] no match in snippet view article
there are a total of ( 2 n1 n ) = ( 2 n1 ) ! n ! ( n1 ) ! {\displaystyle {\binom {2n-1}{n}}={\frac {(2n-1)!}{n!(n-1)!}}} different resamples
Ordinary differential equation (4,751 words) [view diff] no match in snippet view article find links to article
equation of the form F ( x , y , y ′ , … , y ( n1 ) ) = y ( n ) {\displaystyle F\left(x,y,y',\ldots ,y^{(n-1)}\right)=y^{(n)}} is called an explicit ordinary
ISO 216 (3,350 words) [view diff] no match in snippet view article find links to article
as An = S × L, where (measuring in metres) A n = { S = ( 1 2 ) n + 1 2 L = ( 1 2 ) n1 2 {\displaystyle {\text{A}}_{n}={\begin{cases}S=\left({\sqrt {\frac
Thames Estuary (2,658 words) [view diff] no match in snippet view article find links to article
490′N 1°07.750′E / 51.541500°N 1.129167°E / 51.541500; 1.129167 (Knock John No. 5) Knock John № 4 Port buoy Group flashing (3) red 10s 51°32.323′N 1°07
Hypercube (2,045 words) [view diff] no match in snippet view article find links to article
linear recurrence relation E m , n = 2 E m , n1 + E m − 1 , n1 {\displaystyle E_{m,n}=2E_{m,n-1}+E_{m-1,n-1}\!} ,     with E 0 , 0 = 1 {\displaystyle
Case study (4,805 words) [view diff] no match in snippet view article find links to article
or action. A case study does not necessarily have to be one observation (N=1), but may include many observations (one or multiple individuals and entities
Generating function (14,532 words) [view diff] exact match in snippet view article find links to article
_{n=0}^{\infty }n(n-1)s_{n}z^{n}+(1-3z)^{3}\sum _{n=0}^{\infty }n(n-1)(n-2)s_{n}z^{n}\right)\\[4px]&=(n+1)(n+2)(n+3)s_{n}-9n(n+1)(n+2)s_{n-1}+27(n-1)n(n+1
1,000,000,000 (3,232 words) [view diff] no match in snippet view article find links to article
OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation
Light (6,073 words) [view diff] no match in snippet view article find links to article
material and another. It is described by Snell's Law: n 1 sin ⁡ θ 1 = n 2 sin ⁡ θ 2   . {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}\ .} where
Glossary of mathematical symbols (9,607 words) [view diff] no match in snippet view article find links to article
is important and readers might assume either definition, N 1 {\displaystyle \mathbb {N} _{1}} and N 0 {\displaystyle \mathbb {N} _{0}} are used, respectively
Divergence theorem (7,505 words) [view diff] no match in snippet view article find links to article
dx'=\int _{\mathbb {R} ^{n-1}}u(x',g(x'))\,dx'.} Now fix i ∈ { 1 , … , n1 } {\displaystyle i\in \{1,\dots ,n-1\}} . Note that ∫ R n1 ∫ − ∞ g ( x ′ ) u
Orthogonal matrix (4,802 words) [view diff] exact match in snippet view article find links to article
orthogonal matrix quadratically: Q n + 1 = 2 M ( Q n1 M + M T Q n ) − 1 {\displaystyle Q_{n+1}=2M\left(Q_{n}^{-1}M+M^{\mathrm {T} }Q_{n}\right)^{-1}}
Gradient descent (5,311 words) [view diff] no match in snippet view article find links to article
include the sequence γ n = | ( x n − x n1 ) T [ ∇ F ( x n ) − ∇ F ( x n1 ) ] | ‖ ∇ F ( x n ) − ∇ F ( x n1 ) ‖ 2 {\displaystyle \gamma _{n}={\frac
Number (7,755 words) [view diff] no match in snippet view article find links to article
} , and sometimes N 0 {\displaystyle \mathbb {N} _{0}} or N 1 {\displaystyle \mathbb {N} _{1}} when it is necessary to indicate whether the set should
Eutectic system (3,459 words) [view diff] no match in snippet view article find links to article
T 2 − 1 1 − ∑ i = 1 n1 x i − 1 1 − ∑ i = 1 n1 x i − 1 1 − ∑ i = 1 n1 x i − 1 1 − ∑ i = 1 n1 x i − 1 1 − ∑ i = 1 n1 x i − H n ∘ R T 2 ]
Quantum mechanics (11,698 words) [view diff] case mismatch in snippet view article find links to article
the corresponding energy levels are E n = ℏ ω ( n + 1 2 ) . {\displaystyle E_{n}=\hbar \omega \left(n+{1 \over 2}\right).} This is another example illustrating
Runge–Kutta methods (6,696 words) [view diff] exact match in snippet view article find links to article
n + 1 {\displaystyle y_{n+1}} is the RK4 approximation of y ( t n + 1 ) {\displaystyle y(t_{n+1})} , and the next value ( y n + 1 {\displaystyle y_{n+1}}
Homology (mathematics) (6,435 words) [view diff] exact match in snippet view article
n + 1 = 0 n + 1 , n1 , {\displaystyle \partial _{n}\circ \partial _{n+1}=0_{n+1,n-1},} i.e., the constant map sending every element of C n + 1 {\displaystyle
Student's t-distribution (5,734 words) [view diff] no match in snippet view article find links to article
t ( 0 ,   τ 2 = n / ( n1 ) ,   n1 )   . {\displaystyle t_{\mathsf {ML}}\sim {\mathcal {lst}}(0,\ \tau ^{2}=n/(n-1),\ n-1)~.} The location-scale
Velocity (3,414 words) [view diff] no match in snippet view article find links to article
given by the harmonic mean of the speeds v ¯ = n ( 1 v 1 + 1 v 2 + 1 v 3 + ⋯ + 1 v n ) − 1 = n ( ∑ i = 1 n 1 v i ) − 1 . {\displaystyle {\bar {v}}=n\left({1
Manifold (9,476 words) [view diff] no match in snippet view article find links to article
sphere and hyperspheres, are n ( n1 ) / 2 {\displaystyle n(n-1)/2} dimensional manifolds, where n1 {\displaystyle n-1} is the dimension of the sphere
Maxwell–Boltzmann distribution (5,695 words) [view diff] no match in snippet view article find links to article
{mv}{kT}}v^{n-1}+(n-1)v^{n-2}{\biggr ]}=0} This yields the most probable speed (mode) v p = ( n1 ) k T m . {\textstyle v_{\rm {p}}={\sqrt {\frac {(n-1)kT}{m}}}
Low-pass filter (4,293 words) [view diff] no match in snippet view article find links to article
o u t ( ( n1 ) T ) = V i ( 1 − e − ω 0 n T ) − V i ( 1 − e − ω 0 ( ( n1 ) T ) ) {\displaystyle v_{\rm {out}}(nT)-v_{\rm {out}}((n-1)T)=V_{i}(1-e^{-\omega
Pound (force) (1,178 words) [view diff] no match in snippet view article
avoirdupois pound (lb) result in a pound-force equal to 4.4482216152605 N. 1 lbf = 1 lb × g n = 1 lb × 9.80665 m s 2 / 0.3048 m ft ≈ 1 lb × 32.174049 f t s 2 ≈
Orthogonal group (7,813 words) [view diff] no match in snippet view article find links to article
2 q n ( n1 ) ( q n1 ) ∏ i = 1 n1 ( q 2 i − 1 ) , {\displaystyle \left|\operatorname {O} ^{+}(2n,q)\right|=2q^{n(n-1)}\left(q^{n}-1\right)\prod
Fermat number (4,487 words) [view diff] no match in snippet view article find links to article
F n1 − 1 ) 2 + 1 {\displaystyle F_{n}=(F_{n-1}-1)^{2}+1} F n = F 0 ⋯ F n1 + 2 {\displaystyle F_{n}=F_{0}\cdots F_{n-1}+2} for n1, F n = F n
Loan (2,048 words) [view diff] no match in snippet view article find links to article
interest rate c is: P = L ⋅ c ( 1 + c ) n ( 1 + c ) n1 {\displaystyle P=L\cdot {\frac {c\,(1+c)^{n}}{(1+c)^{n}-1}}} For more information, see monthly
Beta distribution (43,410 words) [view diff] no match in snippet view article find links to article
sample excess kurtosis = G 2 = N ( N + 1 ) ( N1 ) ( N − 2 ) ( N − 3 ) ∑ i = 1 N ( Y i − y ¯ ) 4 v ¯ Y 2 − 3 ( N1 ) 2 ( N − 2 ) ( N − 3 ) {\displaystyle
Euler's constant (6,627 words) [view diff] no match in snippet view article find links to article
the pair of series γ = ∑ n = 1N 1 ( n ) + N 0 ( n ) 2 n ( 2 n + 1 ) log ⁡ 4 π = ∑ n = 1N 1 ( n ) − N 0 ( n ) 2 n ( 2 n + 1 ) , {\displaystyle {\begin{aligned}\gamma
Area (5,316 words) [view diff] no match in snippet view article find links to article
y_{i})} (i=0, 1, ..., n-1) of whose n vertices are known, the area is given by the surveyor's formula: A = 1 2 | ∑ i = 0 n1 ( x i y i + 1 − x i + 1
Block cipher (6,542 words) [view diff] exact match in snippet view article find links to article
n + 1 , R n + 1 ) = ( L n + 1 ′ , R n + 1 ′ ) {\displaystyle (L_{n+1},R_{n+1})=(L_{n+1}',R_{n+1}')} . The decryption of a ciphertext ( L n + 1 , R n +
11 (number) (3,183 words) [view diff] no match in snippet view article
numbers n {\displaystyle n} and m {\displaystyle m} where n ! + 1 = m 2 {\displaystyle n!+1=m^{2}} are known; the largest pair (7, 71) satisfies 5041
List of churches preserved by the Churches Conservation Trust in Northern England (2,511 words) [view diff] no match in snippet view article find links to article
or year Notes Grade St Andrew, Bywell Northumberland 54°56′53″N 1°55′34″W / 54.9481°N 1.9260°W / 54.9481; -1.9260 (St Andrew, Bywell) c. 850 The tower
Periodic table (27,127 words) [view diff] exact match in snippet view article find links to article
{\displaystyle v} satisfies the condition v = v N = 1 4 R 2 N ( N + 1 ) {\displaystyle v=v_{N}={\frac {1}{4}}R^{2}N(N+1)} , where N = n + l {\displaystyle N=n+l}
Permutation (10,321 words) [view diff] no match in snippet view article find links to article
formula: P ( n , k ) = n ⋅ ( n1 ) ⋅ ( n − 2 ) ⋯ ( n − k + 1 ) ⏟ k   f a c t o r s {\displaystyle P(n,k)=\underbrace {n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}
Chinese remainder theorem (7,179 words) [view diff] no match in snippet view article find links to article
+ a 2 m 1 n 1 . {\displaystyle x=a_{1}m_{2}n_{2}+a_{2}m_{1}n_{1}.} Indeed, x = a 1 m 2 n 2 + a 2 m 1 n 1 = a 1 ( 1 − m 1 n 1 ) + a 2 m 1 n 1 = a 1 + (
Complete graph (1,218 words) [view diff] no match in snippet view article find links to article
Kuratowski to graph theory. Kn has n(n1)/2 edges (a triangular number), and is a regular graph of degree n1. All complete graphs are their own maximal
Roulette (7,550 words) [view diff] no match in snippet view article find links to article
they employ: ∑ n = 1 ∞ M [ ξ n ] = − 1 37 ∑ n = 1 ∞ r n → − ∞ . {\displaystyle \sum _{n=1}^{\infty }M[\xi _{n}]=-{\frac {1}{37}}\sum _{n=1}^{\infty }r_{n}\to
Phonon (6,669 words) [view diff] exact match in snippet view article find links to article
the nth atom is − 2 C u n + C ( u n + 1 + u n1 ) = m d 2 u n d t 2 . {\displaystyle -2Cu_{n}+C\left(u_{n+1}+u_{n-1}\right)=m{\frac {d^{2}u_{n}}{dt^{2}}}
Shor's algorithm (5,687 words) [view diff] exact match in snippet view article find links to article
2 2 n + 1 {\displaystyle k/2^{2{n}+1}} is accurate to j / r {\displaystyle j/r} by 2 n + 1 {\displaystyle 2n+1} bits. Thus, | j r − k 2 2 n + 1 | ≤ 1
Definite matrix (8,431 words) [view diff] no match in snippet view article find links to article
c} a real constant. In the n = 1 {\displaystyle n=1} case, this is a parabola, and just like in the n = 1 {\displaystyle n=1} case, we have Theorem: This
Complete graph (1,218 words) [view diff] no match in snippet view article find links to article
Kuratowski to graph theory. Kn has n(n1)/2 edges (a triangular number), and is a regular graph of degree n1. All complete graphs are their own maximal
Ergodic theory (3,727 words) [view diff] no match in snippet view article find links to article
have: lim N → ∞ 1 N ∑ n = 0 N1 U n ( I − U ) = lim N → ∞ 1 N ( I − U N ) = 0 {\displaystyle \lim _{N\to \infty }{1 \over N}\sum _{n=0}^{N-1}U^{n}(I-U)=\lim
Set (mathematics) (4,654 words) [view diff] no match in snippet view article
+ … | A n | ) − ( | A 1 ∩ A 2 | + | A 1 ∩ A 3 | + … | A n1 ∩ A n | ) + … + ( − 1 ) n1 ( | A 1 ∩ A 2 ∩ A 3 ∩ … ∩ A n | ) . {\displaystyle
Premier League (18,480 words) [view diff] no match in snippet view article find links to article
2013. The total number of matches can be calculated using the formula n*(n-1) where n is the total number of teams. "Why is there a Saturday football
Coxeter group (3,561 words) [view diff] exact match in snippet view article find links to article
Sn+1; the generators correspond to the transpositions (1 2), (2 3), ... , (n n+1). Any two non-consecutive transpositions commute, while multiplying two consecutive
Power of a test (4,215 words) [view diff] no match in snippet view article find links to article
is B ( θ ) = Pr ( T n > 1.64   |   μ D = θ ) = Pr ( D ¯ n − 0 σ ^ D / n > 1.64   |   μ D = θ ) = Pr ( D ¯ n − θ + θ σ ^ D / n > 1.64   |   μ D = θ ) =
Hamiltonian (quantum mechanics) (4,901 words) [view diff] no match in snippet view article
-particle case: H ^ = ∑ n = 1 N T ^ n + V ^ = ∑ n = 1 N p ^ n ⋅ p ^ n 2 m n + V ( r 1 , r 2 , … , r N , t ) = − ℏ 2 2 ∑ n = 1 N 1 m n ∇ n 2 + V ( r 1 ,
Spearman's rank correlation coefficient (4,159 words) [view diff] exact match in snippet view article find links to article
thus V a r ( U ) = ( n + 1 ) ( 2 n + 1 ) 6 − ( ( n + 1 ) 2 ) 2 = n 2 − 1 12 {\displaystyle \mathrm {Var} (U)=\textstyle {\frac {(n+1)(2n+1)}{6}}-\left(\textstyle
Lambda calculus (11,331 words) [view diff] no match in snippet view article find links to article
Consider the factorial function F(n) recursively defined by F(n) = 1, if n = 0; else n × F(n1). In the lambda expression which is to represent this function
Harmonic mean (5,959 words) [view diff] no match in snippet view article find links to article
x_{n}} is defined to be H ( x 1 , x 2 , … , x n ) = n 1 x 1 + 1 x 2 + ⋯ + 1 x n = n ∑ i = 1 n 1 x i . {\displaystyle H(x_{1},x_{2},\ldots ,x_{n})={\frac
Hydrogen atom (5,791 words) [view diff] no match in snippet view article find links to article
number: it can run only up to n1 {\displaystyle n-1} , i.e., ℓ = 0 , 1 , … , n1 {\displaystyle \ell =0,1,\ldots ,n-1} . Due to angular momentum conservation
Akaike information criterion (5,504 words) [view diff] no match in snippet view article find links to article
! m 1 ! ( m − m 1 ) ! p m 1 ( 1 − p ) m − m 1 ⋅ n ! n 1 ! ( n − n 1 ) ! q n 1 ( 1 − q ) n − n 1 {\displaystyle {\mathcal {L}}(p,q)\,=\,{\frac {m!}{m_{1}
Hydrocarbon (2,580 words) [view diff] exact match in snippet view article find links to article
3 n + 1 2 ) O 2 ⟶ n CO 2 + ( n + 1 ) H 2 O {\displaystyle {\ce {C}}_{n}{\ce {H}}_{2n+2}+\left({{3n+1} \over 2}\right){\ce {O2->}}n{\ce {CO2}}+(n+1){\ce
Quantum field theory (14,854 words) [view diff] no match in snippet view article find links to article
the above example, O(N) has N(N1)/2 continuous symmetries (the dimension of its Lie algebra), while O(N1) has (N1)(N − 2)/2. The number of broken
Time value of money (3,978 words) [view diff] no match in snippet view article find links to article
Where i = g : F V ( A ) = A ⋅ n ( 1 + i ) n1 {\displaystyle FV(A)\,=\,A\cdot n(1+i)^{n-1}} The following table summarizes the different formulas
4 (9,309 words) [view diff] no match in snippet view article find links to article
\\\end{aligned}}} They are defined as locally trivial fibrations that map f : S 2 n1 → S n {\displaystyle f:S^{2n-1}\rightarrow S^{n}} for values of n = 2 ,
Andorra (12,663 words) [view diff] no match in snippet view article find links to article
The New York Times Geographic data related to Andorra at OpenStreetMap Wikimedia Atlas of Andorra 42°33′N 1°35′E / 42.550°N 1.583°E / 42.550; 1.583
Cooperativity (1,951 words) [view diff] no match in snippet view article find links to article
estimations of each cascade's layer, n ≤ n 1 . n 2 {\displaystyle n\leq n_{1}.n_{2}} , where n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are the
Laplace operator (4,056 words) [view diff] no match in snippet view article find links to article
rewritten as: 1 r N1 ∂ ∂ r ( r N1 ∂ f ∂ r ) . {\displaystyle {\frac {1}{r^{N-1}}}{\frac {\partial }{\partial r}}\left(r^{N-1}{\frac {\partial f}{\partial
List of rivers of Yorkshire (1,006 words) [view diff] no match in snippet view article find links to article
54°2′27″N 1°56′35″W / 54.04083°N 1.94306°W / 54.04083; -1.94306 (Mouth of River Dibb) 143 m 469 ft Grimwith Reservoir 54°4′48″N 1°54′41″W / 54.08000°N 1
Modulo (3,348 words) [view diff] no match in snippet view article find links to article
operands. The range of values for an integer modulo operation of n is 0 to n1 (a mod 1 is always 0; a mod 0 is undefined, being a division by zero). When
Graph (discrete mathematics) (3,693 words) [view diff] no match in snippet view article
vertex is n1 (or n + 1 if loops are allowed, because a loop contributes 2 to the degree), and the maximum number of edges is n(n1)/2 (or n(n + 1)/2 if
Prediction interval (2,847 words) [view diff] exact match in snippet view article find links to article
with n – 1 degrees of freedom: X n + 1 s ∼ T n1 . {\displaystyle {\frac {X_{n+1}}{s}}\sim T^{n-1}.} Solving for X n + 1 {\displaystyle X_{n+1}} gives
Standard RAID levels (4,427 words) [view diff] no match in snippet view article find links to article
_{2}\;\oplus \;...\;\oplus \;\mathbf {D} _{n-1}} Q = ⨁ i g i D i = g 0 D 0 ⊕ g 1 D 1 ⊕ g 2 D 2 ⊕ . . . ⊕ g n1 D n1 {\displaystyle \mathbf {Q} =\bigoplus
Σ-algebra (5,312 words) [view diff] no match in snippet view article find links to article
lim sup n → ∞ A n = ⋂ n = 1 ∞ ⋃ m = n ∞ A m = ⋂ n = 1 ∞ A n ∪ A n + 1 ∪ ⋯ . {\displaystyle \limsup _{n\to \infty }A_{n}=\bigcap _{n=1}^{\infty }\bigcup _{m=n}^{\infty
Mutualism (biology) (4,977 words) [view diff] no match in snippet view article
mutualists are quantified as: d N 1 d t = r 1 N 1 − α 11 N 1 2 + β 12 N 1 N 2 d N 2 d t = r 2 N 2 − α 22 N 2 2 + β 21 N 1 N 2 {\displaystyle {\begin{aligned}{\frac
Ghana (14,593 words) [view diff] no match in snippet view article find links to article
conference. Key Development Forecasts for Ghana from International Futures Ghana 2012 Summary Trade Statistics 8°02′N 1°05′W / 8.03°N 1.08°W / 8.03; -1.08
600 (number) (3,861 words) [view diff] exact match in snippet view article
Pentagram number of the form 5 n 2 − 5 n + 1 {\displaystyle 5n^{2}-5n+1} . Hexagram number of the form 6 n 2 − 6 n + 1 {\displaystyle 6n^{2}-6n+1} i.e. a
Quantum harmonic oscillator (6,794 words) [view diff] no match in snippet view article find links to article
] + a † a ) | n ⟩ = ⟨ n | ( N + 1 ) | n ⟩ = n + 1 ⇒ a † | n ⟩ = n + 1 | n + 1 ⟩ ⇒ | n ⟩ = 1 n a † | n1 ⟩ = 1 n ( n1 ) ( a † ) 2 | n − 2 ⟩ = ⋯ =
Chebyshev polynomials (11,111 words) [view diff] no match in snippet view article find links to article
n 2 − 1 T n + 1 − 1 n1 T 1 T n = n n 2 − 1 T n + 1 − 1 2 ( n1 ) ( T n + 1 + T n1 ) = 1 2 ( n + 1 ) T n + 1 − 1 2 ( n1 ) T n1 . {\displaystyle
Mean anomaly (1,324 words) [view diff] no match in snippet view article find links to article
as a series expansion: M = f + 2 ∑ n = 1 ∞ ( − 1 ) n [ 1 n + 1 − e 2 ] β n sin ⁡ n f {\displaystyle M=f+2\sum _{n=1}^{\infty }(-1)^{n}\left[{\frac {1}{n}}+{\sqrt
Inductance (8,469 words) [view diff] no match in snippet view article find links to article
m , n = 1 K i m L m , n d i n = ! ∑ n = 1 K ∂ W ( i ) ∂ i n d i n . {\displaystyle \sum \limits _{m}^{K}i_{m}v_{m}{\text{d}}t=\sum \limits _{m,n=1}^{K}i_{m}L_{m
Radius (1,188 words) [view diff] no match in snippet view article find links to article
n sides of length s is given by r = Rn s, where R n = 1 / ( 2 sin ⁡ π n ) . {\displaystyle R_{n}=1\left/\left(2\sin {\frac {\pi }{n}}\right)\right..}
Lucas number (2,593 words) [view diff] exact match in snippet view article find links to article
following: L n = F n1 + F n + 1 = 2 F n + 1 − F n {\displaystyle L_{n}=F_{n-1}+F_{n+1}=2F_{n+1}-F_{n}} L m + n = L m + 1 F n + L m F n1 {\displaystyle
Cube (algebra) (2,982 words) [view diff] no match in snippet view article
consecutive integers can be expressed as follows: n3 − (n1)3 = 3(n1)n + 1. or (n + 1)3 − n3 = 3(n + 1)n + 1. There is no minimum perfect cube, since the cube
Covariance matrix (5,410 words) [view diff] no match in snippet view article find links to article
x n1 ] [ 1 − ρ x 1 , x 2 ∣ x 3 . . . ⋯ − ρ x 1 , x n ∣ x 2 . . . x n1 − ρ x 2 , x 1 ∣ x 3 . . . 1 ⋯ − ρ x 2 , x n ∣ x 1 , x 3 . . . x n1 ⋮ ⋮
Arqiva (2,485 words) [view diff] no match in snippet view article find links to article
(51°18′28.5″N 1°14′41″W / 51.307917°N 1.24472°W / 51.307917; -1.24472) Haverfordwest Heathfield Holme Moss (53°32′00″N 1°51′29″W / 53.53333°N 1.85806°W
L'Hôpital's rule (6,962 words) [view diff] no match in snippet view article find links to article
interest rates: lim r → 0 P r ( 1 + r ) n ( 1 + r ) n1 = P lim r → 0 ( 1 + r ) n + r n ( 1 + r ) n1 n ( 1 + r ) n1 = P n . {\displaystyle {\begin{aligned}\lim
Fermi–Dirac statistics (4,821 words) [view diff] no match in snippet view article find links to article
¯ i = ∑ n 1 , n 2 , … n i   P n 1 , n 2 , … = ∑ n 1 , n 2 , … n i   e − β ( n 1 ε 1 + n 2 ε 2 + ⋯ + n i ε i + ⋯ ) ∑ n 1 , n 2 , … e − β ( n 1 ε 1 + n
Atrazine (5,303 words) [view diff] no match in snippet view article find links to article
6-triazine 2-Chloro-4-ethylamino-6-isopropylamino-s-triazine 6-Chloro-N-ethyl-N'-(1-methylethyl)-1,3,5-triazine-2,4-diamine Identifiers CAS Number 1912-24-9 Y
Euclidean algorithm (15,008 words) [view diff] no match in snippet view article find links to article
integer r n1 {\displaystyle r_{n-1}} will then be the GCD and we can state gcd ( a , b ) = r n1 {\displaystyle {\text{gcd}}(a,b)=r_{n-1}} . The algorithm
Togo (6,986 words) [view diff] no match in snippet view article find links to article
Wikimedia Atlas of Togo Key Development Forecasts for Togo from International Futures Trade Togo 2012 Summary Trade Statistics 8°N 1°E / 8°N 1°E / 8; 1
Normal (geometry) (2,452 words) [view diff] no match in snippet view article
representation r ( t 1 , … , t n1 ) = p 0 + t 1 p 1 + ⋯ + t n1 p n1 , {\displaystyle \mathbf {r} \left(t_{1},\ldots ,t_{n-1}\right)=\mathbf {p} _{0}+t_{1}\mathbf
Perturbation theory (quantum mechanics) (15,886 words) [view diff] no match in snippet view article
+\lambda \left|n^{(1)}\right\rangle \right)=1} ⟨ n ( 0 ) | n ( 0 ) ⟩ + λ ⟨ n ( 0 ) | n ( 1 ) ⟩ + λ ⟨ n ( 1 ) | n ( 0 ) ⟩ + λ 2 ⟨ n ( 1 ) | n ( 1 ) ⟩ = 1 {\displaystyle
Consistency (2,791 words) [view diff] no match in snippet view article find links to article
R T Φ t 0 ¯ … t n1 ¯ {\displaystyle R^{{\mathfrak {T}}_{\Phi }}{\overline {t_{0}}}\ldots {\overline {t_{n-1}}}} if R t 0 … t n1 ∈ Φ ; {\displaystyle
9 (4,607 words) [view diff] no match in snippet view article find links to article
sum will be nine. In base- N {\displaystyle N} , the divisors of N1 {\displaystyle N-1} have this property. There are other interesting patterns involving
Mean motion (1,900 words) [view diff] no match in snippet view article find links to article
simply one revolution divided by this time, or, n = 2 π P , n = 360 ∘ P , or n = 1 P , {\displaystyle n={\frac {2\pi }{P}},\qquad n={\frac {360^{\circ }}{P}}
Euler method (4,906 words) [view diff] exact match in snippet view article find links to article
is the backward Euler method: y n + 1 = y n + h f ( t n + 1 , y n + 1 ) . {\displaystyle y_{n+1}=y_{n}+hf(t_{n+1},y_{n+1}).} This differs from the (standard
Alkane (5,904 words) [view diff] no match in snippet view article find links to article
alkanes range in complexity from the simplest case of methane (CH4), where n = 1 (sometimes called the parent molecule), to arbitrarily large and complex
Avro Lancaster (15,106 words) [view diff] no match in snippet view article find links to article
53°52′29″N 1°39′36″W / 53.874647°N 1.660124°W / 53.874647; -1.660124 695 Armstrong Whitworth Whitley 52°22′59″N 1°29′26″W / 52.382954°N 1.490615°W
Finite difference method (3,581 words) [view diff] exact match in snippet view article find links to article
) = f ( n + 1 ) ( ξ ) ( n + 1 ) ! ( h ) n + 1 , x 0 < ξ < x 0 + h , {\displaystyle R_{n}(x_{0}+h)={\frac {f^{(n+1)}(\xi )}{(n+1)!}}(h)^{n+1}\,,\quad
Total internal reflection (13,483 words) [view diff] no match in snippet view article find links to article
as‍ n 1 = c / v 1 , {\displaystyle n_{1\!}=c/v_{1}\,,} where c is the speed of light in vacuum.  Hence‍ v 1 = c / n 1 . {\displaystyle v_{1\!}=c/n_{1}\
Normal subgroup (3,163 words) [view diff] no match in snippet view article find links to article
and therefore there is n 1 ′ ∈ N {\displaystyle n_{1}'\in N} such that n 1 a 2 = a 2 n 1 ′ . {\displaystyle n_{1}a_{2}=a_{2}n_{1}'.} This proves that this
Composite number (848 words) [view diff] no match in snippet view article find links to article
number of distinct prime factors. For the latter μ ( n ) = ( − 1 ) 2 x = 1 {\displaystyle \mu (n)=(-1)^{2x}=1} (where μ is the Möbius function and x is half
Perturbation theory (quantum mechanics) (15,886 words) [view diff] no match in snippet view article
+\lambda \left|n^{(1)}\right\rangle \right)=1} ⟨ n ( 0 ) | n ( 0 ) ⟩ + λ ⟨ n ( 0 ) | n ( 1 ) ⟩ + λ ⟨ n ( 1 ) | n ( 0 ) ⟩ + λ 2 ⟨ n ( 1 ) | n ( 1 ) ⟩ = 1 {\displaystyle
Face (geometry) (1,100 words) [view diff] no match in snippet view article
An n-dimensional simplex (line segment (n = 1), triangle (n = 2), tetrahedron (n = 3), etc.), defined by n + 1 vertices, has a face for each subset of
Ellipsis (5,042 words) [view diff] no match in snippet view article find links to article
+ 100   = ∑ n = 1 100 n = 100 ? {\displaystyle 1+2+3+\cdots +100\ =\sum _{n=1}^{100}n=100?} (see termial) 1 × 2 × 3 × ⋯ × 100   = ∏ n = 1 100 n = 100
River Wharfe (3,332 words) [view diff] no match in snippet view article find links to article
21″N 1°57′5.02″W / 54.0508917°N 1.9513944°W / 54.0508917; -1.9513944 Barden Bridge, River Wharfe 54°0′45.32″N 1°55′19.15″W / 54.0125889°N 1.9219861°W
Temperature (12,974 words) [view diff] no match in snippet view article find links to article
number of microstates in the combined system 1 + system 2 is N 1 ⋅ N 2 {\displaystyle N_{1}\cdot N_{2}} , the logarithm of which (times the Boltzmann constant)
Quantum superposition (5,263 words) [view diff] exact match in snippet view article find links to article
differential equation: i d ψ n d t = c ∗ ψ n + 1 + c ψ n1 {\displaystyle i{d\psi _{n} \over dt}=c^{*}\psi _{n+1}+c\psi _{n-1}} In the case in which left and right
Sufficient statistic (6,668 words) [view diff] no match in snippet view article find links to article
1 n ( x 1 n ) = ∏ i = 1 n ( 1 β − α ) 1 { α ≤ x i ≤ β } = ( 1 β − α ) n 1 { α ≤ x i ≤ β , ∀ i = 1 , … , n } = ( 1 β − α ) n 1 { α ≤ min 1 ≤ i ≤ n X i
Cantor set (6,916 words) [view diff] no match in snippet view article find links to article
n1 3 ∪ ( 2 3 + C n1 3 ) = 1 3 ( C n1 ∪ ( 2 + C n1 ) ) {\displaystyle C_{n}:={\frac {C_{n-1}}{3}}\cup \left({\frac {2}{3}}+{\frac {C_{n-1}}{3}}\right)={\frac
Annuity (2,481 words) [view diff] no match in snippet view article find links to article
value is given by: s n ¯ | i = ( 1 + i ) n1 i , {\displaystyle s_{{\overline {n}}|i}={\frac {(1+i)^{n}-1}{i}},} where n {\displaystyle n} is the number
London Symphony Orchestra (8,954 words) [view diff] no match in snippet view article find links to article
The London Symphony Orchestra (LSO) is a British symphony orchestra based in London. Founded in 1904, the LSO is the oldest of London's symphony orchestras
Nth root (4,896 words) [view diff] no match in snippet view article find links to article
n + y n = x + y n x n1 + ( n1 ) y 2 x + ( n + 1 ) y 3 n x n1 + ( 2 n1 ) y 2 x + ( 2 n + 1 ) y 5 n x n1 + ( 3 n1 ) y 2 x + ⋱ . {\displaystyle
Finite difference (5,764 words) [view diff] no match in snippet view article find links to article
h n [ f ] ( x ) = ∑ i = 0 n ( − 1 ) n − i ( n i ) f ( x + i h ) , {\displaystyle \Delta _{h}^{n}[f](x)=\sum _{i=0}^{n}(-1)^{n-i}{\binom {n}{i}}f{\bigl
Rainbow (9,298 words) [view diff] no match in snippet view article find links to article
(wavelength 750nm, n = 1.330 based on the dispersion relation of water), the radius angle is 42.5°; for blue light (wavelength 350nm, n = 1.343), the radius
Taylor's theorem (9,587 words) [view diff] no match in snippet view article find links to article
n1 ) ( a ) ( a − a ) n1 ( n1 ) ! = 0 G ( a ) = ( a − a ) n = 0 {\displaystyle {\begin{aligned}F(a)&=f(a)-f(a)-f'(a)(a-a)-...-{\frac {f^{(n-1
Fundamental theorem of calculus (5,063 words) [view diff] no match in snippet view article find links to article
) + [ − F ( x n1 ) + F ( x n1 ) ] + ⋯ + [ − F ( x 1 ) + F ( x 1 ) ] − F ( x 0 ) = [ F ( x n ) − F ( x n1 ) ] + [ F ( x n1 ) − F ( x n − 2
List of unsolved problems in mathematics (19,482 words) [view diff] no match in snippet view article find links to article
of the shortest addition chain producing 2 n1 {\displaystyle 2^{n}-1} is at most n1 {\displaystyle n-1} plus the length of the shortest addition
Williams Grand Prix Engineering (14,911 words) [view diff] no match in snippet view article find links to article
51°37′5″N 1°24′46″W / 51.61806°N 1.41278°W / 51.61806; -1.41278 Formula One portal Williams Grand Prix Engineering Limited, currently racing in Formula
Symmetric group (6,031 words) [view diff] no match in snippet view article find links to article
transpositions: }}} ( n n1 ) ( n1 n − 2 ) ⋯ ( 2 1 ) ( n1 n − 2 ) ( n − 2 n − 3 ) ⋯ , {\displaystyle (n\,n-1)(n-1\,n-2)\cdots (2\,1)(n-1\,n-2)(n-2\,n-3)\cdots
Tetration (6,860 words) [view diff] no match in snippet view article find links to article
n := { 1 if  n = 0 , a a ↑↑ ( n1 ) if  n > 0 , {\displaystyle {a\uparrow \uparrow n}:={\begin{cases}1&{\text{if }}n=0,\\a^{a\uparrow \uparrow (n-1)}&{\text{if
Mathematical proof (4,616 words) [view diff] exact match in snippet view article find links to article
an odd number. But (2n − 1) + 2 = 2n + 1 = 2(n+1) − 1, so 2(n+1) − 1 is odd (P(n+1)). So P(n) implies P(n+1). Thus 2n − 1 is odd, for all positive integers
Ellipse (15,658 words) [view diff] no match in snippet view article find links to article
π a [ 1 − ∑ n = 1 ∞ ( ( 2 n1 ) ! ! ( 2 n ) ! ! ) 2 e 2 n 2 n1 ] = − 2 π a ∑ n = 0 ∞ ( ( 2 n1 ) ! ! ( 2 n ) ! ! ) 2 e 2 n 2 n1 , {\displaystyle
Hypergeometric distribution (3,974 words) [view diff] no match in snippet view article find links to article
K n − k ) ( N n ) = 1 , {\displaystyle \sum _{0\leq k\leq {\textrm {min}}(n,K)}{{K \choose k}{N-K \choose n-k} \over {N \choose n}}=1,} which essentially
Range (statistics) (1,233 words) [view diff] no match in snippet view article
g ( x ) [ G ( x + t ) − G ( x ) ] n1 d x . {\displaystyle F(t)=n\int _{-\infty }^{\infty }g(x)[G(x+t)-G(x)]^{n-1}\,{\text{d}}x.} Gumbel notes that
Jackknife resampling (2,104 words) [view diff] no match in snippet view article find links to article
aggregating the parameter estimates from each subsample of size ( n1 ) {\displaystyle (n-1)} obtained by omitting one observation. The jackknife technique
Order statistic (4,485 words) [view diff] exact match in snippet view article find links to article
= 1 ( N + 1 ) g ( 0 ) + 1 ( N + 1 ) ( N + 2 ) ∫ 0 1 Q ″ ( z ) δ N + 1 ( z ) d z {\displaystyle E(Y_{(1)})={\frac {1}{(N+1)g(0)}}+{\frac {1}{(N+1)(N+2)}}\int
Tensor (9,329 words) [view diff] exact match in snippet view article find links to article
, v n , v n + 1 , … , v n + m ) = S ( v 1 , … , v n ) T ( v n + 1 , … , v n + m ) , {\displaystyle (S\otimes T)(v_{1},\ldots ,v_{n},v_{n+1},\ldots ,v_{n+m})=S(v_{1}
England (21,899 words) [view diff] no match in snippet view article find links to article
UK – official website of the British Government Geographic data related to England at OpenStreetMap 53°08′N 1°23′W / 53.13°N 1.38°W / 53.13; -1.38
Error function (7,242 words) [view diff] no match in snippet view article find links to article
x = e − x 2 x π ( 1 + ∑ n = 1 ∞ ( − 1 ) n 1 ⋅ 3 ⋅ 5 ⋯ ( 2 n1 ) ( 2 x 2 ) n ) = e − x 2 x π ∑ n = 0 ∞ ( − 1 ) n ( 2 n1 ) ! ! ( 2 x 2 ) n , {\displaystyle
Lists of integrals (5,617 words) [view diff] exact match in snippet view article find links to article
non-integrable singularity at 0 for n ≤ −1: ∫ x n d x = x n + 1 n + 1 + C (for  n ≠ − 1 ) {\displaystyle \int x^{n}\,dx={\frac {x^{n+1}}{n+1}}+C\qquad {\text{(for }}n\neq
JPEG (13,261 words) [view diff] no match in snippet view article find links to article
divided into N 8×8 blocks B 0 , B 1 , B 2 , . . . , B n1 {\displaystyle B_{0},B_{1},B_{2},...,B_{n-1}} , then a 3-scan progressive encoding encodes DC
List of tallest structures in the United Kingdom (1,076 words) [view diff] no match in snippet view article find links to article
52°22′26.89″N 1°11′17.35″W / 52.3741361°N 1.1881528°W / 52.3741361; -1.1881528 (Rugby VLF Mast); 52°22′16.24″N 1°11′5.63″W / 52.3711778°N 1.1848972°W
Moment (mathematics) (3,099 words) [view diff] no match in snippet view article
said not to exist. If the n-th moment about any point exists, so does the (n1)-th moment (and thus, all lower-order moments) about every point. The zeroth
Blaise Pascal (6,606 words) [view diff] no match in snippet view article find links to article
 3, ... and n = 1, 2, 3, ... The generator t00 = 1. Pascal concluded with the proof, t m n = ( m + n ) ( m + n1 ) ⋯ ( m + 1 ) n ( n1 ) ⋯ 1 . {\displaystyle
Exponential function (5,859 words) [view diff] no match in snippet view article find links to article
valid for all complex values of x {\displaystyle x} : exp ⁡ x = lim n → ∞ ( 1 + x n ) n . {\displaystyle \exp x=\lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}
Transition metal (4,504 words) [view diff] no match in snippet view article find links to article
radium. The f-block elements La–Yb and Ac–No have chemical activity of the (n1)d shell, but importantly also have chemical activity of the (n−2)f shell
Magic square (22,234 words) [view diff] exact match in snippet view article find links to article
( n + 1 − i ) {\displaystyle (n+1-i)} and ( n + 1 − j ) {\displaystyle (n+1-j)} are exchanged where i < j < n + 1 2 {\displaystyle i<j<{\frac {n+1}{2}}}
Quantifier (logic) (4,529 words) [view diff] no match in snippet view article
x n1 , y ) ∧ A ( x 1 , … , x n1 , z ) ⟹ y = z ) . {\displaystyle \forall y,z{\big (}A(x_{1},\ldots ,x_{n-1},y)\wedge A(x_{1},\ldots ,x_{n-1},z)\implies
PageRank (9,082 words) [view diff] no match in snippet view article find links to article
where R is the solution of the equation R = [ ( 1 − d ) / N ( 1 − d ) / N ⋮ ( 1 − d ) / N ] + d [ ℓ ( p 1 , p 1 ) ℓ ( p 1 , p 2 ) ⋯ ℓ ( p 1 , p
Chain rule (7,085 words) [view diff] no match in snippet view article find links to article
the composite function f 1 ∘ ( f 2 ∘ ⋯ ( f n1 ∘ f n ) ) {\displaystyle f_{1}\circ (f_{2}\circ \cdots (f_{n-1}\circ f_{n}))\!} , if each function f i {\displaystyle
Simple Lie group (2,247 words) [view diff] no match in snippet view article find links to article
SL(n) of n by n matrices with determinant equal to 1 is simple for all n > 1. The first classification of simple Lie groups was by Wilhelm Killing, and
Cao Cao (30,343 words) [view diff] no match in snippet view article find links to article
Cited in Chen and Pei 429, 1.46 n. 1 (second n. 1). Pei Songzhi in Chen and Pei 429, 1.46 n. 1 (second n. 1): "臣松之以為今之虛封蓋自此始。" Book of Wei: "始置奉常宗正官。"
Moons of Neptune (4,348 words) [view diff] no match in snippet view article find links to article
current position when Triton was captured. Neptune's outermost moon S/2021 N 1, which has an orbital period of about 27 Earth years, orbits farther from
Pythagorean triple (11,390 words) [view diff] no match in snippet view article find links to article
n1 − a n − 2 + 2 {\displaystyle a_{n}=6a_{n-1}-a_{n-2}+2} with a 1 = 3 {\displaystyle a_{1}=3} and a 2 = 20 {\displaystyle a_{2}=20} b n = 6 b n
Real analysis (7,673 words) [view diff] no match in snippet view article find links to article
non-absolutely is ∑ n = 1 ∞ ( − 1 ) n1 n = 1 − 1 2 + 1 3 − 1 4 + ⋯ = ln ⁡ 2. {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n-1}}{n}}=1-{\frac {1}{2}}+{\frac
Poisson distribution (10,943 words) [view diff] no match in snippet view article find links to article
(\lambda _{n})} where λ 1 + λ 2 + ⋯ + λ n = 1 , {\displaystyle \lambda _{1}+\lambda _{2}+\dots +\lambda _{n}=1,} then ( X 1 , X 2 , … , X n ) {\displaystyle
Srinivasa Ramanujan (11,059 words) [view diff] no match in snippet view article find links to article
previously unknown identities, such as ( 1 + 2 ∑ n = 1 ∞ cos ⁡ ( n θ ) cosh ⁡ ( n π ) ) − 2 + ( 1 + 2 ∑ n = 1 ∞ cosh ⁡ ( n θ ) cosh ⁡ ( n π ) ) − 2 = 2 Γ 4
Mortgage (7,195 words) [view diff] no match in snippet view article find links to article
following formula: A = P ⋅ r ( 1 + r ) n ( 1 + r ) n1 {\displaystyle A=P\cdot {\frac {r(1+r)^{n}}{(1+r)^{n}-1}}} where: A {\displaystyle A} is the periodic
Moons of Neptune (4,348 words) [view diff] no match in snippet view article find links to article
current position when Triton was captured. Neptune's outermost moon S/2021 N 1, which has an orbital period of about 27 Earth years, orbits farther from
Real analysis (7,673 words) [view diff] no match in snippet view article find links to article
non-absolutely is ∑ n = 1 ∞ ( − 1 ) n1 n = 1 − 1 2 + 1 3 − 1 4 + ⋯ = ln ⁡ 2. {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n-1}}{n}}=1-{\frac {1}{2}}+{\frac
Irrational number (5,420 words) [view diff] no match in snippet view article find links to article
polynomial equations p ( x ) = a n x n + a n1 x n1 + ⋯ + a 1 x + a 0 = 0 , {\displaystyle p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{1}x+a_{0}=0\;,} where
Vector space (11,557 words) [view diff] no match in snippet view article find links to article
} but ‖ x n1 = ∑ i = 1 2 n 2 − n = 2 n ⋅ 2 − n = 1. {\displaystyle \|\mathbf {x} _{n}\|_{1}=\sum _{i=1}^{2^{n}}2^{-n}=2^{n}\cdot 2^{-n}=1.} More generally
Spithead (243 words) [view diff] no match in snippet view article find links to article
50°45′05″N 1°08′12″W / 50.75140°N 1.13667°W / 50.75140; -1.13667 Spithead is an area of the Solent and a roadstead off Gilkicker Point in Hampshire
List of Star Wars starfighters (6,317 words) [view diff] no match in snippet view article find links to article
accidentally steals a Naboo N-1 starfighter and pilots it into the Droid Control Ship's docking bay, destroying the vessel from the inside. N-1 starfighters also
Leonhard Euler (10,214 words) [view diff] no match in snippet view article find links to article
elaborate argument in 1741): ∑ n = 1 ∞ 1 n 2 = lim n → ∞ ( 1 1 2 + 1 2 2 + 1 3 2 + ⋯ + 1 n 2 ) = π 2 6 . {\displaystyle \sum _{n=1}^{\infty }{1 \over n^{2}}=\lim
Correlation (5,122 words) [view diff] no match in snippet view article find links to article
Γ ( N −   1   2 )   ⋅ ( 1 − r 2 )   N   − 2   2 ⋅ ( 1 − ρ 2 )   N − 3   2 ⋅ ( 1 − r ρ ) − N +   3   2 ⋅ F H y p (     3   2 , −   1   2 ; N −   1   2
Linear differential equation (4,757 words) [view diff] no match in snippet view article find links to article
n y ( n ) ( x ) + a n1 x n1 y ( n1 ) ( x ) + ⋯ + a 0 y ( x ) = 0 , {\displaystyle x^{n}y^{(n)}(x)+a_{n-1}x^{n-1}y^{(n-1)}(x)+\cdots +a_{0}y(x)=0
Monoid (4,447 words) [view diff] no match in snippet view article find links to article
1, 2, ..., n1} given by [ 0 1 2 ⋯ n − 2 n1 1 2 3 ⋯ n1 k ] {\displaystyle {\begin{bmatrix}0&1&2&\cdots &n-2&n-1\\1&2&3&\cdots &n-1&k\end{bmatrix}}}
Oxford (9,841 words) [view diff] no match in snippet view article find links to article
university town of the past. Oxford's latitude and longitude are 51°45′N 1°15′W / 51.750°N 1.250°W / 51.750; -1.250, with Ordnance Survey grid reference SP513061
Formetorex (280 words) [view diff] no match in snippet view article find links to article
Formetorex Names Preferred IUPAC name N-(1-Phenylpropan-2-yl)formamide Other names Formetorex N-Formylamphetamine N-(alpha-Methylphenethyl)formamide Identifiers
Two's complement (5,379 words) [view diff] no match in snippet view article find links to article
N-bit integer a N1 a N − 2 … a 0 {\displaystyle a_{N-1}a_{N-2}\dots a_{0}} is given by the following formula: w = − a N1 2 N1 + ∑ i = 0 N − 2
Norm (mathematics) (5,666 words) [view diff] exact match in snippet view article
{\displaystyle \ell ^{2}} distance. The set of vectors in R n + 1 {\displaystyle \mathbb {R} ^{n+1}} whose Euclidean norm is a given positive constant forms
Channel Tunnel (15,935 words) [view diff] no match in snippet view article find links to article
51°00′45″N 1°30′15″E / 51.0125°N 1.5041°E / 51.0125; 1.5041 Status Active Start Folkestone, Kent, England, (51°05′50″N 1°09′21″E / 51.0971°N 1.1558°E
Spherical harmonics (12,442 words) [view diff] no match in snippet view article find links to article
n1 ∂ ∂ r + r − 2 Δ S n1 = ∂ 2 ∂ r 2 + n1 r ∂ ∂ r + r − 2 Δ S n1 {\displaystyle \nabla ^{2}=r^{1-n}{\frac {\partial }{\partial r}}r^{n-1}{\frac
Rao–Blackwell theorem (2,164 words) [view diff] no match in snippet view article find links to article
θ ^ B A Y E S = n + 1 n [ 1 − ( X ( 1 ) 1 − k ) ( X ( n ) 1 + k ) − 1 [ ( X ( 1 ) 1 − k ) ( X ( n ) 1 + k ) ] n + 1 − 1 ] X ( n ) 1 + k {\displaystyle
Function (mathematics) (10,612 words) [view diff] exact match in snippet view article
{\displaystyle f} can be defined by the formula f ( n ) = n + 1 {\displaystyle f(n)=n+1} , for n ∈ { 1 , 2 , 3 } {\displaystyle n\in \{1,2,3\}} . When a function
Collusion (3,738 words) [view diff] no match in snippet view article find links to article
n ( 1 − δ ) {\displaystyle 1\geq n(1-\delta )} 1 ≥ n − n δ {\displaystyle 1\geq n-n\delta } n δ ≥ n1 {\displaystyle n\delta \geq n-1} δ ≥ n1 n
Estimation theory (2,557 words) [view diff] no match in snippet view article find links to article
\left[x[0]\right]=A} and E [ A ^ 2 ] = E [ 1 N ∑ n = 0 N1 x [ n ] ] = 1 N [ ∑ n = 0 N1 E [ x [ n ] ] ] = 1 N [ N A ] = A {\displaystyle \mathrm {E} \left[{\hat
Electrostatics (2,558 words) [view diff] no match in snippet view article find links to article
× 10 − 12   C 2 ⋅ N1 ⋅ m − 2 . {\displaystyle \varepsilon _{0}\approx \mathrm {8.854\ 187\ 817\times 10^{-12}~C^{2}{\cdot }N^{-1}{\cdot }m^{-2}} .}
Elliptic Curve Digital Signature Algorithm (2,831 words) [view diff] no match in snippet view article find links to article
{\displaystyle d_{A}} , randomly selected in the interval [ 1 , n1 ] {\displaystyle [1,n-1]} ; and a public key curve point Q A = d A × G {\displaystyle
Empirical distribution function (1,934 words) [view diff] no match in snippet view article find links to article
is defined as F ^ n ( t ) = number of elements in the sample ≤ t n = 1 n ∑ i = 1 n 1 X i ≤ t , {\displaystyle {\widehat {F}}_{n}(t)={\frac {{\mbox{number
Orientability (3,514 words) [view diff] no match in snippet view article find links to article
the above homology group is isomorphic to H n1 ( S n1 ; Z ) ≅ Z {\displaystyle H_{n-1}\left(S^{n-1};\mathbf {Z} \right)\cong \mathbf {Z} } . A choice
List of tallest buildings and structures (4,047 words) [view diff] no match in snippet view article find links to article
Clock Tower  United Kingdom Birmingham 100 328 1908 52°27′00″N 1°55′51″W / 52.4499°N 1.9307°W / 52.4499; -1.9307 Wooden building Ascent MKE  United
Toulouse FC (1,411 words) [view diff] no match in snippet view article find links to article
Ground Stadium de Toulouse Capacity 33,150 Coordinates 43°34′59″N 1°26′3″E / 43.58306°N 1.43417°E / 43.58306; 1.43417 Owner RedBird Capital Partners (85%)
List of Sites of Special Scientific Interest in Suffolk (9,704 words) [view diff] no match in snippet view article find links to article
52°10′N 1°0′E / 52.167°N 1.000°E / 52.167; 1.000 (Suffolk) Suffolk is a county in East Anglia. It is bounded by Norfolk to the north, Cambridgeshire
Confidence interval (4,617 words) [view diff] no match in snippet view article find links to article
{X}}={\frac {X_{1}+\cdots +X_{n}}{n}},} S 2 = 1 n1 ∑ i = 1 n ( X i − X ¯ ) 2 . {\displaystyle S^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}.}
Burkina Faso (16,510 words) [view diff] no match in snippet view article find links to article
Futures. Burkina Faso Business Facts from Bizpages World Bank 2011 Trade Summary for Burkiana Faso 12°20′N 1°50′W / 12.333°N 1.833°W / 12.333; -1.833
Uninterruptible power supply (6,163 words) [view diff] no match in snippet view article find links to article
equivalent to one very large UPS. "N + 1" means that if the load can be supplied by N modules, the installation will contain N + 1 modules. In this way, failure
Derivative (7,187 words) [view diff] no match in snippet view article find links to article
{\displaystyle n} -th derivative as the derivative of the ( n1 ) {\displaystyle (n-1)} -th derivative or the derivative of order n {\displaystyle
Q Sharp (1,751 words) [view diff] no match in snippet view article find links to article
$V_j$ when controlled by n-qubit number state $\ket{j}$. /// /// $U = \sum^{N-1}_{j=0}\ket{j}\bra{j}\otimes V_j$. /// /// # Input /// ## unitaryGenerator
Convergent series (2,028 words) [view diff] no match in snippet view article find links to article
powers of any n>1 produce a convergent series: 1 1 + 1 n + 1 n 2 + 1 n 3 + 1 n 4 + 1 n 5 + ⋯ = n n1 . {\displaystyle {1 \over 1}+{1 \over n}+{1 \over n^{2}}+{1
OSI model (5,432 words) [view diff] no match in snippet view article find links to article
N1, where it is known as the service data unit (SDU). At layer N1 the SDU is concatenated with a header, a footer, or both, producing a layer N1 PDU
Root of unity (5,939 words) [view diff] no match in snippet view article find links to article
a positive integer, is a number z satisfying the equation z n = 1. {\displaystyle z^{n}=1.} Unless otherwise specified, the roots of unity may be taken
Nottingham (11,841 words) [view diff] no match in snippet view article find links to article
Location in Europe Show map of Europe Coordinates: 52°57′22″N 1°09′04″W / 52.9561°N 1.1512°W / 52.9561; -1.1512 OS grid reference SK 5711 4020 Sovereign
Valence electron (2,333 words) [view diff] no match in snippet view article find links to article
the orbitals of the incomplete (n1)d subshell are included, and for lanthanides and actinides incomplete (n−2)f and (n1)d subshells. The orbitals involved
Centroid (4,177 words) [view diff] no match in snippet view article find links to article
x n1 , y n1 ) , {\displaystyle (x_{n-1},y_{n-1}),} is the point ( C x , C y ) , {\displaystyle (C_{x},C_{y}),} where C x = 1 6 A ∑ i = 0 n1 (
Graph theory (6,394 words) [view diff] no match in snippet view article find links to article
of order n, the maximum degree of each vertex is n1 and the maximum size of the graph is n(n1)/2. The edges of an undirected simple graph permitting
Scientific notation (5,323 words) [view diff] no match in snippet view article find links to article
10^{n_{0}}} and x 1 = m 1 × 10 n 1 {\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} with n 0 = n 1 {\displaystyle n_{0}=n_{1}} Next, add or subtract the significands:
Inverse trigonometric functions (10,715 words) [view diff] no match in snippet view article find links to article
z 7 7 + ⋯ = ∑ n = 0 ∞ ( 2 n1 ) ! ! ( 2 n ) ! ! z 2 n + 1 2 n + 1 = ∑ n = 0 ∞ ( 2 n ) ! ( 2 n n ! ) 2 z 2 n + 1 2 n + 1 ; | z | ≤ 1 {\displaystyle
Stochastic approximation (4,147 words) [view diff] exact match in snippet view article find links to article
the following structure: θ n + 1 − θ n = a n ( α − N ( θ n ) ) , θ ¯ n = 1 n ∑ i = 0 n1 θ i {\displaystyle \theta _{n+1}-\theta _{n}=a_{n}(\alpha -N(\theta
Leeds United F.C. (10,873 words) [view diff] no match in snippet view article find links to article
1919) Ground Elland Road Capacity 37,608 Coordinates 53°46′40″N 1°34′20″W / 53.77778°N 1.57222°W / 53.77778; -1.57222 Owner 49ers Enterprises Chairman
Standing wave (6,571 words) [view diff] no match in snippet view article find links to article
the boundary condition restricts the wavelength of the standing waves to n = 1 , 2 , 3 , … {\displaystyle n=1,2,3,\ldots } Waves can only form standing
Martingale (probability theory) (2,839 words) [view diff] no match in snippet view article
Yn : n = 1, 2, 3, ... } is a martingale with respect to { Xn : n = 1, 2, 3, ... }. To show this E [ Y n + 1 ∣ X 1 , … , X n ] = p ( q / p ) X n + 1 + q
Root mean square (2,662 words) [view diff] no match in snippet view article find links to article
{\displaystyle T} is the sampling period, ∑ n = 1 N x 2 [ n ] = 1 N ∑ m = 1 N | X [ m ] | 2 , {\displaystyle \sum _{n=1}^{N}{x^{2}[n]}={\frac {1}{N}}\sum
Countable set (4,437 words) [view diff] exact match in snippet view article find links to article
numbers. This can be achieved using the assignments n ↔ n + 1 {\displaystyle n\leftrightarrow n+1} and n ↔ 2 n {\displaystyle n\leftrightarrow 2n} , so
Tangent (4,078 words) [view diff] no match in snippet view article find links to article
the curve is then g = u n + u n1 z + ⋯ + u 1 z n1 + u 0 z n = 0. {\displaystyle g=u_{n}+u_{n-1}z+\dots +u_{1}z^{n-1}+u_{0}z^{n}=0.\,} Applying the
Root mean square (2,662 words) [view diff] no match in snippet view article find links to article
{\displaystyle T} is the sampling period, ∑ n = 1 N x 2 [ n ] = 1 N ∑ m = 1 N | X [ m ] | 2 , {\displaystyle \sum _{n=1}^{N}{x^{2}[n]}={\frac {1}{N}}\sum
Centroid (4,177 words) [view diff] no match in snippet view article find links to article
x n1 , y n1 ) , {\displaystyle (x_{n-1},y_{n-1}),} is the point ( C x , C y ) , {\displaystyle (C_{x},C_{y}),} where C x = 1 6 A ∑ i = 0 n1 (
Force India (7,110 words) [view diff] no match in snippet view article find links to article
52°04′33″N 1°01′46″W / 52.07583°N 1.02944°W / 52.07583; -1.02944 Force India Formula One Team Limited, commonly known as Force India and later Sahara
Circle (5,861 words) [view diff] no match in snippet view article find links to article
the form | x a | n + | y b | n = 1 {\displaystyle \left|{\frac {x}{a}}\right|^{n}\!+\left|{\frac {y}{b}}\right|^{n}\!=1} for positive a, b, and n. A supercircle
Countable set (4,437 words) [view diff] exact match in snippet view article find links to article
numbers. This can be achieved using the assignments n ↔ n + 1 {\displaystyle n\leftrightarrow n+1} and n ↔ 2 n {\displaystyle n\leftrightarrow 2n} , so
Wave interference (4,612 words) [view diff] no match in snippet view article find links to article
= N1 {\displaystyle n=N-1} , where φ n − φ n1 = 2 π N . {\displaystyle \varphi _{n}-\varphi _{n-1}={\frac {2\pi }{N}}.} To show that ∑ n = 0 N
Standard error (2,690 words) [view diff] no match in snippet view article find links to article
: FPC): FPC = N − n N1 {\displaystyle \operatorname {FPC} ={\sqrt {\frac {N-n}{N-1}}}} which, for large N: FPC ≈ 1 − n N = 1 − f {\displaystyle \operatorname
Stochastic approximation (4,147 words) [view diff] exact match in snippet view article find links to article
the following structure: θ n + 1 − θ n = a n ( α − N ( θ n ) ) , θ ¯ n = 1 n ∑ i = 0 n1 θ i {\displaystyle \theta _{n+1}-\theta _{n}=a_{n}(\alpha -N(\theta
Fermat's Last Theorem (11,703 words) [view diff] no match in snippet view article find links to article
equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions
Zipf's law (4,688 words) [view diff] no match in snippet view article find links to article
to the element of rank k (counting from 1) the probability f ( k ; N ) = 1 H N 1 k {\displaystyle f(k;N)={\frac {1}{H_{N}}}\,{\frac {1}{k}}} where HN
Kronecker delta (4,056 words) [view diff] no match in snippet view article find links to article
n = 1 2 π i ∮ | z | = 1 z x − n1 d z = 1 2 π ∫ 0 2 π e i ( x − n ) φ d φ {\displaystyle \delta _{x,n}={\frac {1}{2\pi i}}\oint _{|z|=1}z^{x-n-1}\
Tagus (353 words) [view diff] no match in snippet view article find links to article
Station: Texas A&M University Press. p. 87, 97, 100. ISBN 9781585443901. OCLC 56517607. 40°19′11″N 1°41′51″W / 40.31972°N 1.69750°W / 40.31972; -1.69750
On-Line Encyclopedia of Integer Sequences (5,561 words) [view diff] exact match in snippet view article find links to article
-3480, -576 OFFSET 1,2 COMMENTS B(n+2) = -B(n)*((n+2)*(n+1)/(4*Pi^2))*z(n+2)/z(n) = -B(n)*((n+2)*(n+1)/(4*Pi^2)) * Sum_{j>=1} a(j)/j^(n+2). Apart from signs
Gloucestershire Warwickshire Railway (2,227 words) [view diff] no match in snippet view article find links to article
Railway Cotswold Steam Preservation Ltd. - Owners of No. 2807 Warwickshire Railways 51°59′21″N 1°55′41″W / 51.98910°N 1.92813°W / 51.98910; -1.92813
Grade II* listed buildings in Nottinghamshire (182 words) [view diff] no match in snippet view article find links to article
Annesley Statue 1832 12 October 1988 SK5109953620 53°04′39″N 1°14′19″W / 53.077371°N 1.238687°W / 53.077371; -1.238687 (Church of All Saints) 1275939
Divisor function (3,734 words) [view diff] no match in snippet view article find links to article
n = 1 ∞ q n σ a ( n ) = ∑ n = 1 ∞ ∑ j = 1 ∞ n a q j n = ∑ n = 1 ∞ n a q n 1 − q n {\displaystyle \sum _{n=1}^{\infty }q^{n}\sigma _{a}(n)=\sum _{n=1}^{\infty
A27 road (3,053 words) [view diff] no match in snippet view article find links to article
list 51°00′44″N 1°40′51″W / 51.0123°N 1.6809°W / 51.0123; -1.6809 (Junction between A27 and A36) 50°59′00″N 1°30′22″W / 50.9834°N 1.5060°W / 50
Trapezoidal rule (3,449 words) [view diff] no match in snippet view article find links to article
{\displaystyle [a,b]} such that a = x 0 < x 1 < ⋯ < x N1 < x N = b {\displaystyle a=x_{0}<x_{1}<\cdots <x_{N-1}<x_{N}=b} and Δ x k {\displaystyle \Delta x_{k}}
Vector calculus (2,122 words) [view diff] no match in snippet view article find links to article
defined (generalizations in other dimensionalities either require n1 {\displaystyle n-1} vectors to yield 1 vector, or are alternative Lie algebras, which
Q–Q plot (2,496 words) [view diff] no match in snippet view article find links to article
(n + 1 − 2a) for some value of a in the range from 0 to 1, which gives a range between k / (n + 1) and (k − 1) / (n1). Expressions include: k / (n +
Discrete uniform distribution (672 words) [view diff] exact match in snippet view article find links to article
variance of 1 k ( N − k ) ( N + 1 ) ( k + 2 ) ≈ N 2 k 2  for small samples  k ≪ N {\displaystyle {\frac {1}{k}}{\frac {(N-k)(N+1)}{(k+2)}}\approx {\frac
Indian mathematics (13,473 words) [view diff] exact match in snippet view article find links to article
n + 1 ) {\displaystyle f_{i}(n+1)} , (for n odd, and i = 1, 2, 3) for the series: π 4 ≈ 1 − 1 3 + 1 5 − ⋯ + ( − 1 ) ( n1 ) / 2 1 n + ( − 1 ) ( n +
Block matrix (3,464 words) [view diff] no match in snippet view article find links to article
form A = [ B 1 C 1 ⋯ 0 A 2 B 2 C 2 ⋱ ⋱ ⋱ ⋮ A k B k C k ⋮ ⋱ ⋱ ⋱ A n1 B n1 C n1 0 ⋯ A n B n ] {\displaystyle \mathbf {A} ={\begin{bmatrix}\mathbf
1 + 2 + 3 + 4 + ⋯ (4,231 words) [view diff] exact match in snippet view article find links to article
series is the triangular number ∑ k = 1 n k = n ( n + 1 ) 2 , {\displaystyle \sum _{k=1}^{n}k={\frac {n(n+1)}{2}},} which increases without bound as n goes
Cleveland, Yorkshire (519 words) [view diff] no match in snippet view article find links to article
54°30′00″N 1°08′02″W / 54.500°N 1.134°W / 54.500; -1.134 Cleveland /ˈkliːvlənd/ is a land of hills and dales from the River Tees to Vale of Pickering
Partition of a set (1,882 words) [view diff] exact match in snippet view article find links to article
partitions of an n-element set is the Catalan number C n = 1 n + 1 ( 2 n n ) . {\displaystyle C_{n}={1 \over n+1}{2n \choose n}.} Wikimedia Commons has media related
0.999... (12,910 words) [view diff] no match in snippet view article find links to article
numbers implies 0. ( 9 ) n + 1 / 10 n = 1 , 0. ( 9 ) n < 1 , {\displaystyle {\begin{aligned}0.(9)_{n}+1/10^{n}&=1,\\0.(9)_{n}&<1,\end{aligned}}} for every
Proteus (moon) (1,822 words) [view diff] no match in snippet view article
discovery, Proteus received the temporary provisional designation S/1989 N 1. Stephen P. Synnott and Bradford A. Smith announced its discovery on July
Cauchy stress tensor (8,309 words) [view diff] no match in snippet view article find links to article
non-symmetric. This also is the case when the Knudsen number is close to one, K n1 {\displaystyle K_{n}\rightarrow 1} , or the continuum is a non-Newtonian
Gamma distribution (8,535 words) [view diff] no match in snippet view article find links to article
least two samples: N ≥ 2 {\displaystyle N\geq 2} , because for N = 1 {\displaystyle N=1} , the function ℓ ( k ) {\displaystyle \ell (k)} increases without
Coefficient of determination (6,308 words) [view diff] no match in snippet view article find links to article
e. dftot = n − 1. Inserting the degrees of freedom and using the definition of R2, it can be rewritten as: R ¯ 2 = 1 − ( 1 − R 2 ) n1 n − p − 1 {\displaystyle
Orthogonal frequency-division multiplexing (11,276 words) [view diff] no match in snippet view article find links to article
{\displaystyle M} , 0 ≤ n ≤ N1 {\displaystyle 0\leq n\leq N-1} . One takes the N {\displaystyle N} -point IFFT of X n , 0 ≤ n ≤ N1 {\displaystyle {\bf {X}}_{n}
Pigeonhole principle (4,044 words) [view diff] no match in snippet view article find links to article
to n1, there are n possible holes. On the other hand, either the "0" hole, the "n1" hole, or both must be empty, for it is impossible (if n > 1) for
Field (mathematics) (10,362 words) [view diff] no match in snippet view article
the elements of E(x) have the form ∑ k = 0 n1 a k x k ,     a k ∈ E . {\displaystyle \sum _{k=0}^{n-1}a_{k}x^{k},\ \ a_{k}\in E.} For example, the
Asymptote (4,505 words) [view diff] exact match in snippet view article find links to article
{-(\cos({\tfrac {1}{x}})+1)}{x^{2}}}} . For the sequence of points x n = ( − 1 ) n ( 2 n + 1 ) π , {\displaystyle x_{n}={\frac {(-1)^{n}}{(2n+1)\pi }},\quad
Diagonal (1,900 words) [view diff] exact match in snippet view article find links to article
by ( n 4 ) + ( n1 2 ) = ( n1 ) ( n − 2 ) ( n 2 − 3 n + 12 ) 24 . {\displaystyle {\binom {n}{4}}+{\binom {n-1}{2}}={\frac {(n-1)(n-2)(n^{2}-3n+12)}{24}}
Separable space (2,071 words) [view diff] no match in snippet view article find links to article
dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle \{x_{n}\}_{n=1}^{\infty }} of elements of the space such that every nonempty
Matrix (mathematics) (13,140 words) [view diff] no match in snippet view article
≤ i ≤ m − 1 {\displaystyle 0\leq i\leq m-1} and 0 ≤ j ≤ n1 {\displaystyle 0\leq j\leq n-1} . This article follows the more common convention in mathematical
23 (number) (4,002 words) [view diff] no match in snippet view article
an Eisenstein prime with no imaginary part and real part of the form 3 n1. {\displaystyle 3n-1.} It is also the fifth Sophie Germain prime and the
Rank correlation (2,523 words) [view diff] exact match in snippet view article find links to article
{E} [U^{2}]=\textstyle {\frac {(n+1)(2n+1)}{6}}} and thus V a r ( U ) = ( n + 1 ) ( 2 n + 1 ) 6 − ( n + 1 ) ( n + 1 ) 4 = n 2 − 1 12 {\displaystyle \mathrm
Numeral system (2,845 words) [view diff] no match in snippet view article find links to article
of the form: ( a n a n1 ⋯ a 1 a 0 . c 1 c 2 c 3 ⋯ ) b = ∑ k = 0 n a k b k + ∑ k = 1 ∞ c k b − k . {\displaystyle (a_{n}a_{n-1}\cdots a_{1}a_{0}.c_{1}c_{2}c_{3}\cdots
List of Sites of Special Scientific Interest in Dorset (930 words) [view diff] no match in snippet view article find links to article
1991 AONB, SAC Map River Avon System Y 475.9 1,176.1 51°01′34″N 1°45′36″W / 51.026°N 1.76°W / 51.026; -1.76 (River Avon System)     SU169252 1996 NCR
Binary tree (5,125 words) [view diff] no match in snippet view article find links to article
{\displaystyle C_{0}=1} , and C n = ∑ i = 0 n1 C i C n1 − i {\displaystyle \textstyle C_{n}=\sum _{i=0}^{n-1}C_{i}C_{n-1-i}} for any positive integer n. It
Bayes estimator (3,819 words) [view diff] exact match in snippet view article find links to article
_{i})} , one is interested in estimating θ n + 1 {\displaystyle \theta _{n+1}} based on x n + 1 {\displaystyle x_{n+1}} . Assume that the θ i {\displaystyle
Pentagonal number (923 words) [view diff] no match in snippet view article find links to article
number: p n = T n1 + n 2 = T n + 2 T n1 = T 2 n1 − T n1 {\displaystyle p_{n}=T_{n-1}+n^{2}=T_{n}+2T_{n-1}=T_{2n-1}-T_{n-1}} Generalized pentagonal
Newcastle United F.C. (10,881 words) [view diff] no match in snippet view article find links to article
1892) Ground St James' Park Capacity 52,305 Coordinates 54°58′32″N 1°37′17″W / 54.9756°N 1.6215°W / 54.9756; -1.6215 Owners Public Investment Fund (80%)
63 (number) (2,273 words) [view diff] no match in snippet view article
, except for when n = 1 {\displaystyle n=1} , a − b = 1 ; {\displaystyle a-b=1;\;} with a n − b n = 1 {\displaystyle a^{n}-b^{n}=1} having no prime divisors
Partial autocorrelation function (1,129 words) [view diff] no match in snippet view article find links to article
= 1 n1 ϕ n1 , k ρ ( n − k ) 1 − ∑ k = 1 n1 ϕ n1 , k ρ ( k ) {\displaystyle \phi _{n,n}={\frac {\rho (n)-\sum _{k=1}^{n-1}\phi _{n-1,k}\rho
Ratio test (5,508 words) [view diff] no match in snippet view article find links to article
test (or "criterion") for the convergence of a series ∑ n = 1 ∞ a n , {\displaystyle \sum _{n=1}^{\infty }a_{n},} where each term is a real or complex
Coxeter–Dynkin diagram (2,810 words) [view diff] no match in snippet view article find links to article
rank are: det(A1n = [2n−1]) = 2n (Finite for all n) det(An = [3n−1]) = n + 1 (finite for all n) det(Bn = [4,3n−2]) = 2 (finite for all n) det(Dn = [3n−3
Dimension (3,894 words) [view diff] no match in snippet view article find links to article
element in the first cover) such that no point is included in more than n + 1 elements. In this case dim X = n. For X a manifold, this coincides with
Commitment scheme (7,696 words) [view diff] no match in snippet view article find links to article
, . . . , p n1 {\displaystyle p_{0},p_{1},...,p_{n-1}} be the coefficients of p {\displaystyle p} , such that p ( x ) = ∑ i = 0 n1 p i x i {\textstyle
Legendre polynomials (5,182 words) [view diff] exact match in snippet view article find links to article
recursion formula ( n + 1 ) P n + 1 ( x ) = ( 2 n + 1 ) x P n ( x ) − n P n1 ( x ) . {\displaystyle (n+1)P_{n+1}(x)=(2n+1)xP_{n}(x)-nP_{n-1}(x)\,.} This relation
Julius Caesar (15,967 words) [view diff] no match in snippet view article find links to article
Iul., 81–82. Tempest 2017, p. 3–4, 261 n. 1; Meier 1995, p. 486 (reporting 23 wounds). Tempest 2017, p. 261 n. 1 cites all ancient accounts: Nic. Dam.
Hilbert space (17,519 words) [view diff] no match in snippet view article find links to article
converges: ∑ n = 1 ∞ | z n | 2 {\displaystyle \sum _{n=1}^{\infty }|z_{n}|^{2}} The inner product on l2 is defined by: ⟨ z , w ⟩ = ∑ n = 1 ∞ z n w n ¯
63 (number) (2,273 words) [view diff] no match in snippet view article
, except for when n = 1 {\displaystyle n=1} , a − b = 1 ; {\displaystyle a-b=1;\;} with a n − b n = 1 {\displaystyle a^{n}-b^{n}=1} having no prime divisors
Multinomial distribution (4,303 words) [view diff] no match in snippet view article find links to article
distribution is the set { ( n 1 , … , n k ) ∈ N k ∣ n 1 + ⋯ + n k = n } . {\displaystyle \{(n_{1},\dots ,n_{k})\in \mathbb {N} ^{k}\mid n_{1}+\cdots +n_{k}=n\}
Algebraic equation (2,162 words) [view diff] no match in snippet view article find links to article
unknown x ( E ) a n x n + a n1 x n1 + ⋯ + a 1 x + a 0 = 0 {\displaystyle (\mathrm {E} )\qquad a_{n}x^{n}+a_{n-1}x^{n-1}+\dots +a_{1}x+a_{0}=0} , with
Ratio test (5,508 words) [view diff] no match in snippet view article find links to article
test (or "criterion") for the convergence of a series ∑ n = 1 ∞ a n , {\displaystyle \sum _{n=1}^{\infty }a_{n},} where each term is a real or complex
Von Neumann–Bernays–Gödel set theory (15,521 words) [view diff] exact match in snippet view article find links to article
n + 1 [ x n + 1 ∧ … ] {\displaystyle \exists x_{n+1}[x_{n+1}\land \dots ]} become ∃ x n + 1 [ x n + 1 ∈ V ∧ … ] , {\displaystyle \exists x_{n+1}[x_{n+1}\in
Hyperbolic space (1,510 words) [view diff] exact match in snippet view article find links to article
2 + ⋯ + x n 2 − x n + 1 2 {\displaystyle q(x)=x_{1}^{2}+\cdots +x_{n}^{2}-x_{n+1}^{2}} on R n + 1 {\displaystyle \mathbb {R} ^{n+1}} , its restriction
Harmonic (2,206 words) [view diff] no match in snippet view article find links to article
these frequencies is periodic at 50 Hz. An nth characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristic
QR code (8,649 words) [view diff] no match in snippet view article find links to article
that these polynomials are all on the form ∏ i = 0 n1 ( x − α i ) {\textstyle \prod _{i=0}^{n-1}(x-\alpha ^{i})} , however the rules for selecting
Arithmetic function (7,508 words) [view diff] no match in snippet view article find links to article
second product gives τ ( n ) = d ( n ) = ( 1 + a 1 ) ( 1 + a 2 ) ⋯ ( 1 + a ω ( n ) ) . {\displaystyle \tau (n)=d(n)=(1+a_{1})(1+a_{2})\cdots (1+a_{\omega
1998 FIFA World Cup (7,663 words) [view diff] no match in snippet view article find links to article
Capacity: 41,300 Nantes Stade de la Beaujoire 47°15′20.27″N 1°31′31.35″W / 47.2556306°N 1.5253750°W / 47.2556306; -1.5253750 (Stade de la Beaujoire)
Orbital mechanics (5,820 words) [view diff] no match in snippet view article find links to article
= { ∑ n = 1 ∞ M n 3 n ! lim θ → 0 ( d n1 d θ n1 [ ( θ θ − sin ⁡ ( θ ) 3 ) n ] ) , ϵ = 1 ∑ n = 1 ∞ M n n ! lim θ → 0 ( d n1 d θ n1 [ ( θ θ
Random variable (6,396 words) [view diff] no match in snippet view article find links to article
function that maps the pair to the sum: X ( ( n 1 , n 2 ) ) = n 1 + n 2 {\displaystyle X((n_{1},n_{2}))=n_{1}+n_{2}} and (if the dice are fair) has a probability
Ordinal number (6,709 words) [view diff] no match in snippet view article find links to article
If n is finite, the n-th number class has cardinality ℵ n1 {\displaystyle \aleph _{n-1}} . If α ≥ ω, the α-th number class has cardinality ℵ α {\displaystyle
Riemann integral (5,354 words) [view diff] no match in snippet view article find links to article
is, max ( x i + 1 − x i ) , i ∈ [ 0 , n1 ] . {\displaystyle \max \left(x_{i+1}-x_{i}\right),\quad i\in [0,n-1].} A tagged partition P(x, t) of an interval
Cauchy sequence (3,218 words) [view diff] exact match in snippet view article find links to article
differences a n + 1 − a n = n + 1n = 1 n + 1 + n < 1 2 n {\displaystyle a_{n+1}-a_{n}={\sqrt {n+1}}-{\sqrt {n}}={\frac {1}{{\sqrt {n+1}}+{\sqrt {n}}}}<{\frac
Negative binomial distribution (8,221 words) [view diff] no match in snippet view article find links to article
0.4 ) 5 0.4 n − 5 = ( n1 n − 5 ) 3 5 2 n − 5 5 n . {\displaystyle f(n)={(n-5)+5-1 \choose n-5}\;(1-0.4)^{5}\;0.4^{n-5}={n-1 \choose n-5}\;3^{5}\;{\frac
Expression (mathematics) (956 words) [view diff] no match in snippet view article
to the complex: f ( a ) + ∑ k = 1 n 1 k ! d k d t k | t = 0 f ( u ( t ) ) + ∫ 0 1 ( 1 − t ) n n ! d n + 1 d t n + 1 f ( u ( t ) ) d t . {\displaystyle
Spline (mathematics) (4,679 words) [view diff] no match in snippet view article
Si(x) for i = 0, …, n1. These must satisfy: S i ( x i ) = y i = S i − 1 ( x i ) , i = 1 ,   … ,   n1 , S 0 ( x 0 ) = y 0 , S n1 ( x n ) = y n , S
Twin prime (2,628 words) [view diff] exact match in snippet view article find links to article
that p n + 1 − p n = m {\displaystyle p_{n+1}-p_{n}=m} for all m < N and so for n large enough we have p n + 1 − p n > N , {\displaystyle p_{n+1}-p_{n}>N
Hyperplane (1,336 words) [view diff] exact match in snippet view article find links to article
translation b ~ ∈ R n + 1 {\displaystyle {\tilde {b}}\in \mathbb {R} ^{n+1}} as the set of all x ∈ R n + 1 {\displaystyle x\in \mathbb {R} ^{n+1}} such that n
Random number generation (4,433 words) [view diff] exact match in snippet view article find links to article
n + 1 = ( a X n + b ) mod m {\displaystyle X_{n+1}=(aX_{n}+b)\,{\textrm {mod}}\,m} to generate numbers, where a, b and m are large integers, and X n +
Pyramid (geometry) (1,422 words) [view diff] no match in snippet view article
regular pyramid. For the pyramid with an n-sided regular base, it has n + 1 vertices, n + 1 faces, and 2n edges. Such pyramid has isosceles triangles as its
Energy level (2,831 words) [view diff] no match in snippet view article find links to article
the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray
List of Sites of Special Scientific Interest in Norfolk (11,471 words) [view diff] no match in snippet view article find links to article
from the original on 16 March 2018. Retrieved 24 June 2018. 52°40′N 1°00′E / 52.667°N 1.000°E / 52.667; 1.000 Ratcliffe, Derek, ed. (1977). A Nature Conservation
R (programming language) (7,947 words) [view diff] no match in snippet view article
data points. s = ∑ ( x i − x ¯ ) 2 n1 {\displaystyle s={\sqrt {\frac {\sum \left(x_{i}-{\bar {x}}\right)^{2}}{n-1}}}} Suppose a sample of four observations
Python (programming language) (13,245 words) [view diff] no match in snippet view article
ValueError('You must enter a non-negative integer') factorial = 1 for i in range(2, n + 1): factorial *= i print(factorial) Python's large standard library provides
M40 motorway (3,452 words) [view diff] no match in snippet view article find links to article
51°43′29″N 1°03′27″W / 51.7246°N 1.0575°W / 51.7246; -1.0575 (M40, J7) 48.0 48.4 77.3 77.9 No Exit J8 Oxford, Cheltenham A40 51°43′56″N 1°04′36″W
Credit default swap (15,043 words) [view diff] no match in snippet view article find links to article
has a default event, in which case it ends with a payment of N ( 1 − R ) {\displaystyle N(1-R)} shown in red, where R {\displaystyle R} is the recovery
Linear equation (2,137 words) [view diff] no match in snippet view article find links to article
linear equation in n variables form a hyperplane (a subspace of dimension n1) in the Euclidean space of dimension n. Linear equations occur frequently
River Avon, Hampshire (1,559 words) [view diff] no match in snippet view article find links to article
51°20′56″N 1°56′53″W / 51.349°N 1.948°W / 51.349; -1.948 The River Avon (/ˈeɪvən/) is in the south of England, rising in Wiltshire, flowing through
Bose–Einstein condensate (9,796 words) [view diff] no match in snippet view article find links to article
{\displaystyle f} the fugacity and g α ( f ) = ∑ n = 1 ∞ f n n α {\displaystyle g_{\alpha }(f)=\sum \limits _{n=1}^{\infty }{\frac {f^{n}}{n^{\alpha }}}} It
Grade I listed buildings in Derbyshire (196 words) [view diff] no match in snippet view article find links to article
Mill Earlier than 1803 3 February 1966 SK3454248081 53°01′44″N 1°29′11″W / 53.028907°N 1.486415°W / 53.028907; -1.486415 (North Mill) Built by William
0 (7,839 words) [view diff] no match in snippet view article find links to article
that for an array of n items the sequence of array indices runs from 0 to n1.[citation needed] There can be confusion between 0- and 1-based indexing;
Geometric distribution (3,608 words) [view diff] no match in snippet view article find links to article
k^{n}\\&{}=p\operatorname {Li} _{-n}(1-p)&({\text{for }}n\neq 0)\end{aligned}}} where Li − n ⁡ ( 1 − p ) {\displaystyle \operatorname {Li} _{-n}(1-p)} is the polylogarithm
Homological algebra (3,857 words) [view diff] exact match in snippet view article find links to article
C n + 1 ⟶ d n + 1 C n ⟶ d n C n1 ⟶ d n1 ⋯ , d n ∘ d n + 1 = 0. {\displaystyle C_{\bullet }:\cdots \longrightarrow C_{n+1}{\stackrel {d_{n+1}}{\longrightarrow
Continuous function (9,400 words) [view diff] no match in snippet view article find links to article
neighborhood N 1 ( f ( c ) ) {\displaystyle N_{1}(f(c))} there is a neighborhood N 2 ( c ) {\displaystyle N_{2}(c)} in its domain such that f ( x ) ∈ N 1 ( f (
List of tallest buildings and structures in the Birmingham Metropolitan Area, West Midlands (10,702 words) [view diff] no match in snippet view article find links to article
Telecommunication Jewellery Quarter Post Office Tower GPO Tower 52°29′01″N 1°54′15″W / 52.483547°N 1.904303°W / 52.483547; -1.904303 2 Birmingham 2 The Mercian
Zhuge Liang (25,943 words) [view diff] no match in snippet view article find links to article
52.1232 n. 1, biography of Zhuge Jin. Ying, Fengsu Tongyi: "葛嬰為陳涉將軍,有功而誅,孝文帝追錄,封其孫諸縣侯,因幷氏焉。此與吳書所說不同。" Cited in Chen and Pei 429, 52.1232 n. 1, biography
Lehmann–Scheffé theorem (984 words) [view diff] no match in snippet view article find links to article
estimator: θ ^ BAYES = n + 1 n [ 1 − X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) − 1 ( X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) ) n + 1 − 1 ] X ( n ) 1 + k {\displaystyle
Hydrolysis (2,267 words) [view diff] no match in snippet view article find links to article
M ( H 2 O ) n1 ( OH ) ( m − 1 ) + + H 3 O + {\displaystyle {\ce {M(H2O)_{\mathit {n}}^{{\mathit {m}}+}{}+H2O<=>M(H2O)_{{\mathit {n}}-1}(OH)^{({\mathit
Gravitational constant (5,177 words) [view diff] no match in snippet view article find links to article
G c 4 ≈ 2.0766 × 10 − 43 N1 . {\displaystyle \kappa ={\frac {8\pi G}{c^{4}}}\approx 2.0766\times 10^{-43}\mathrm {\,N^{-1}} .} The gravitational constant
Tower of Hanoi (6,998 words) [view diff] no match in snippet view article find links to article
Since n is odd (n = 1), it is one peg to the left, i.e. on the left peg. Disk four is 1, so it is on another peg. Since n is odd (n = 1), it is one peg
Schrödinger equation (10,112 words) [view diff] no match in snippet view article find links to article
take the values n = 1 , 2 , 3 , … , {\displaystyle n=1,2,3,\dots ,} ℓ = 0 , 1 , 2 , … , n1 , {\displaystyle \ell =0,1,2,\dots ,n-1,} m = − ℓ , … ,
Discriminant (6,196 words) [view diff] no match in snippet view article find links to article
derivative, A ′ ( x ) = n a n x n1 + ( n1 ) a n1 x n − 2 + ⋯ + a 1 , {\displaystyle A'(x)=na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\cdots +a_{1},} is a
Discriminant (6,196 words) [view diff] no match in snippet view article find links to article
derivative, A ′ ( x ) = n a n x n1 + ( n1 ) a n1 x n − 2 + ⋯ + a 1 , {\displaystyle A'(x)=na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\cdots +a_{1},} is a
Affine space (7,220 words) [view diff] no match in snippet view article find links to article
space of dimension 2 is an affine plane. An affine subspace of dimension n1 in an affine space or a vector space of dimension n is an affine hyperplane
List of Sites of Special Scientific Interest in Hampshire (6,009 words) [view diff] no match in snippet view article find links to article
Conservation Review. Vol. 2. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-21403-2. 51°03′28″N 1°18′29″W / 51.0577°N 1.3081°W / 51.0577; -1.3081
River Swale (2,883 words) [view diff] no match in snippet view article find links to article
54°22′50.16″N 1°59′15.05″W / 54.3806000°N 1.9875139°W / 54.3806000; -1.9875139 Barney Beck 54°22′53.87″N 1°58′37.77″W / 54.3816306°N 1.9771583°W
Binomial regression (2,055 words) [view diff] no match in snippet view article find links to article
binary regression can be considered a binomial regression with n = 1 {\displaystyle n=1} , or a regression on ungrouped binary data, while a binomial regression
Compact space (5,645 words) [view diff] no match in snippet view article find links to article
interval (0, 1) is not compact: the open cover ( 1 n , 1 − 1 n ) {\textstyle \left({\frac {1}{n}},1-{\frac {1}{n}}\right)} for n = 3, 4, ...  does not
European Community number (637 words) [view diff] no match in snippet view article find links to article
is the following sum modulo 11: R = ( N 1 + 2 N 2 + 3 N 3 + 4 N 4 + 5 N 5 + 6 N 6 ) mod 1 1 {\displaystyle R=(N_{1}+2N_{2}+3N_{3}+4N_{4}+5N_{5}+6N_{6}){\bmod
Lehmann–Scheffé theorem (984 words) [view diff] no match in snippet view article find links to article
estimator: θ ^ BAYES = n + 1 n [ 1 − X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) − 1 ( X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) ) n + 1 − 1 ] X ( n ) 1 + k {\displaystyle
Average (3,241 words) [view diff] no match in snippet view article find links to article
n 1 x 1 + 1 x 2 + ⋯ + 1 x n {\displaystyle {\frac {n}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}}} argmin x ∈ R ≠ 0 ∑ i = 1 n (
Pythagorean theorem (12,742 words) [view diff] no match in snippet view article find links to article
simplex, the square of the (n − 1)-content of the facet opposing the right vertex will equal the sum of the squares of the (n − 1)-contents of the remaining
Europe (21,821 words) [view diff] no match in snippet view article find links to article
25.5 E −9.6 16.5 2.7 Arkhangelsk 64.5 N 40.5 E −12.7 16.3 1.3 Lerwick 60 N 1 W 3.5 12.4 7.4 Stockholm 59.5 N 19 E −1.7 18.4 7.4 Helsinki 60 N 25 E −4
Uniform convergence (5,084 words) [view diff] exact match in snippet view article find links to article
can be found such that each of the functions f N , f N + 1 , f N + 2 , … {\displaystyle f_{N},f_{N+1},f_{N+2},\ldots } differs from f {\displaystyle f}
History of calculus (5,929 words) [view diff] no match in snippet view article find links to article
n1 ( 1 − x ) n1 d x {\displaystyle \int _{0}^{1}x^{n-1}(1-x)^{n-1}\,dx} ∫ 0 ∞ e − x x n1 d x {\displaystyle \int _{0}^{\infty }e^{-x}x^{n-1}\
Free fall (2,500 words) [view diff] no match in snippet view article find links to article
) = ∑ n = 1 ∞ [ lim r → 0 ( x n n ! d n1 d r n1 [ r n ( 7 2 ( arcsin ⁡ ( r ) − r − r 2 ) ) − 2 3 n ] ) ] . {\displaystyle y(t)=\sum _{n=1}^{\infty
Chromadorea (447 words) [view diff] no match in snippet view article find links to article
molecular markers are found in essential proteins such as tRNA (guanine-N(1))-methyltransferase and can serve as a reliable molecular method of distinguishing
Haskell (4,530 words) [view diff] exact match in snippet view article find links to article
and widely used. So-called n+k patterns (definitions of the form fact (n+1) = (n+1) * fact n) were no longer allowed. This syntactic sugar had misleading
Drugs controlled by the German Betäubungsmittelgesetz (315 words) [view diff] no match in snippet view article find links to article
(6-Dimethylamino-4,4-diphenyl-heptan-3-yl)acetat α-Methylacetylfentanyl N-Phenyl-N-[1-(1-phenyl-propan-2-yl)-4-piperidyl]acetamid Allylescaline 4-Allyloxy-3
Git (6,882 words) [view diff] no match in snippet view article find links to article
N − 1 is its default ancestor. However, when there is no like-named file in revision N − 1, Git searches for a file that existed only in revision N − 1
Product rule (4,116 words) [view diff] no match in snippet view article find links to article
value, n + 1, we have d d x x n + 1 = d d x ( x n ⋅ x ) = x d d x x n + x n d d x x (the product rule is used here) = x ( n x n1 ) + x n1 (the induction
Chanel (7,024 words) [view diff] no match in snippet view article find links to article
Blanc Le Lift Sublimage Blue Serum La Solution 10 de Chanel Vamp Nail Polish N°1 line (skincare and makeup products based on holistic beauty and eco-friendly
Car (8,923 words) [view diff] no match in snippet view article find links to article
University. 28 June 2003. Archived from the original on 28 June 2003. "car, n.1". OED Online. Oxford University Press. September 2014. Archived from the
Gas (6,356 words) [view diff] no match in snippet view article find links to article
4 dm3/mol (liters per mole). The relation is given by V 1 n 1 = V 2 n 2 , {\displaystyle {\frac {V_{1}}{n_{1}}}={\frac {V_{2}}{n_{2}}},} where n is the amount
Alnwick Infirmary (621 words) [view diff] no match in snippet view article find links to article
55°24′32″N 1°49′39″W / 55.408827°N 1.827563°W / 55.408827; -1.827563 John Lambert was a local solicitor. Alnwick Infirmary 1819 building - 55°24′51″N 1°42′37″W
Sinc function (2,956 words) [view diff] no match in snippet view article find links to article
product-to-sum identity ∏ n = 1 k cos ⁡ ( x 2 n ) = 1 2 k − 1 ∑ n = 1 2 k − 1 cos ⁡ ( n1 / 2 2 k − 1 x ) , ∀ k ≥ 1 , {\displaystyle \prod _{n=1}^{k}\cos \left({\frac
East Anglia (3,012 words) [view diff] no match in snippet view article find links to article
and Lowestoft Enterprise Zone Alconbury Enterprise Campus. Archived 16 January 2016 at the Wayback Machine. 52°30′N 1°00′E / 52.5°N 1°E / 52.5; 1
Dihedral group (3,439 words) [view diff] no match in snippet view article find links to article
∣ s 2 = 1 , t 2 = 1 , ( s t ) n = 1 ⟩ . {\displaystyle \mathrm {D} _{n}=\left\langle s,t\mid s^{2}=1,t^{2}=1,(st)^{n}=1\right\rangle .} In particular
Planck constant (7,635 words) [view diff] no match in snippet view article find links to article
and n ∈ { 1 , 2 , 3 , . . . } {\displaystyle n\in \{1,2,3,...\}} . Once the electron reached the lowest energy level ( n = 1 {\displaystyle n=1} ), it
M42 motorway (1,023 words) [view diff] no match in snippet view article find links to article
coordinates) 52°20′56″N 1°48′35″W / 52.3488°N 1.8097°W / 52.3488; -1.8097 (Junction 3a) Termination point M40 52°28′39″N 1°42′39″W / 52.4774°N 1.7109°W / 52
Bose–Einstein statistics (6,020 words) [view diff] exact match in snippet view article find links to article
sublevel, therefore w ( n , 1 ) = 1 {\displaystyle w(n,1)=1} . It is easy to see that there are ( n + 1 ) {\displaystyle (n+1)} ways of distributing n
Automobiles Alpine (4,677 words) [view diff] no match in snippet view article find links to article
49°54′44″N 1°05′06″E / 49.9121346°N 1.0849268°E / 49.9121346; 1.0849268 The Société des Automobiles Alpine SAS, commonly known as Alpine (French pronunciation:
Cross-correlation (4,084 words) [view diff] no match in snippet view article find links to article
f ⋆ g ) [ n ]   ≜ ∑ m = 0 N1 f [ m ] ¯ g [ ( m + n ) mod   N ] {\displaystyle (f\star g)[n]\ \triangleq \sum _{m=0}^{N-1}{\overline {f[m]}}g[(m+n)_{{\text{mod}}~N}]}
Grade II* listed buildings in South Yorkshire (114 words) [view diff] no match in snippet view article find links to article
Barnsley House c. 1670 18 April 1985 SE4103609639 53°34′54″N 1°22′54″W / 53.581744°N 1.381653°W / 53.581744; -1.381653 (Grimethorpe Hall) 1151202
Wishart distribution (4,094 words) [view diff] no match in snippet view article find links to article
1 − 1 X ) / 2 2 n 1 p 1 / 2 | V 1 | n 1 / 2 Γ p 1 ( n 1 2 ) ] = n 1 p 1 2 log ⁡ 2 + n 1 2 log ⁡ | V 1 | + log ⁡ Γ p 1 ( n 1 2 ) − n 1 − p 1 − 1 2 E p
Washington Double Star Catalog (312 words) [view diff] no match in snippet view article find links to article
star with n components will be represented by entries in the catalog for n-1 pairs of stars. The database used to construct the WDS originated at Lick
Network topology (5,208 words) [view diff] no match in snippet view article find links to article
grows quadratically with the number of nodes: c = n ( n1 ) 2 . {\displaystyle c={\frac {n(n-1)}{2}}.\,} This makes it impractical for large networks
55 (number) (951 words) [view diff] no match in snippet view article
and fifth, where the first two Fermat primes of the form 2 2 n + 1 {\displaystyle 2^{2^{n}}+1} are 3 {\displaystyle 3} and 5 {\displaystyle 5} (11 is also
Figurate number (1,340 words) [view diff] case mismatch in snippet view article find links to article
) = n 1 = ( n + 0 1 ) = ( n 1 ) {\displaystyle P_{1}(n)={\frac {n}{1}}={\binom {n+0}{1}}={\binom {n}{1}}} (linear numbers), P 2 ( n ) = n ( n + 1 ) 2
Butterfly effect (4,874 words) [view diff] exact match in snippet view article find links to article
parametrization of the logistic map: x n + 1 = 4 x n ( 1 − x n ) , 0 ≤ x 0 ≤ 1 , {\displaystyle x_{n+1}=4x_{n}(1-x_{n}),\quad 0\leq x_{0}\leq 1,} which
Homotopy group (3,417 words) [view diff] no match in snippet view article find links to article
fibration S O ( n1 ) → S O ( n ) → S O ( n ) / S O ( n1 ) ≅ S n1 {\displaystyle SO(n-1)\to SO(n)\to SO(n)/SO(n-1)\cong S^{n-1}} giving the long
Sorting algorithm (6,396 words) [view diff] no match in snippet view article find links to article
Other notes In-place merge sort — — n log 2 ⁡ n {\displaystyle n\log ^{2}n} 1 Yes Merging Can be implemented as a stable sort based on stable in-place
Exterior derivative (3,088 words) [view diff] no match in snippet view article find links to article
(n1)-form ω V = v 1 ( d x 2 ∧ ⋯ ∧ d x n ) − v 2 ( d x 1 ∧ d x 3 ∧ ⋯ ∧ d x n ) + ⋯ + ( − 1 ) n1 v n ( d x 1 ∧ ⋯ ∧ d x n1 ) = ∑ i = 1 n ( − 1 )
Group (mathematics) (13,114 words) [view diff] no match in snippet view article
theory of groups, as depending on the symbolic equation θ n = 1 {\displaystyle \theta ^{n}=1} (1854) gives the first abstract definition of a finite group
Z-transform (4,524 words) [view diff] no match in snippet view article find links to article
origin "punched out". Let x [ n ] = − ( .5 ) n u [ − n1 ] {\displaystyle x[n]=-(.5)^{n}\,u[-n-1]} (where u {\displaystyle u} is the Heaviside step function)
Italy (35,637 words) [view diff] no match in snippet view article find links to article
5, Statuto speciale per il Trentino-Alto Adige L. cost. 31 gennaio 1963, n. 1, Statuto speciale della Regione Friuli-Venezia Giulia "Ready for Ratification"
Alternating series (1,655 words) [view diff] exact match in snippet view article find links to article
the natural logarithm: ∑ n = 1 ∞ ( − 1 ) n + 1 n x n = ln ⁡ ( 1 + x ) . {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}x^{n}\;=\;\ln(1+x).}
Stirling numbers of the second kind (4,007 words) [view diff] exact match in snippet view article find links to article
that a partition of the n + 1 {\displaystyle n+1} objects into k nonempty subsets either contains the ( n + 1 ) {\displaystyle (n+1)} -th object as a singleton
Random matrix (5,660 words) [view diff] exact match in snippet view article find links to article
λ n < λ n + 1 < … {\displaystyle \lambda _{1}<\ldots <\lambda _{n}<\lambda _{n+1}<\ldots } , one defines the normalized spacings s = ( λ n + 1 − λ n )
Silkworm (missile) (970 words) [view diff] no match in snippet view article
SY-1 License produced version of the P-15 Termit. NATO reporting name CSS-N-1 Scrubbrush. SY-2 HY-1 NATO reporting names CSS-N-2 Safflower(ship-based)
Phased array (5,021 words) [view diff] no match in snippet view article find links to article
accordingly[page needed]: A F = ∑ n = 1 N I n 1 [ ∑ m = 1 M I m 1 e j ( m − 1 ) ( k d x sin ⁡ θ cos ⁡ ϕ + β x ) ] e j ( n1 ) ( k d y sin ⁡ θ sin ⁡ ϕ + β
79 (number) (535 words) [view diff] exact match in snippet view article
1 79 = ∑ n = 1 ∞ P ( n ) × 10 − ( n + 1 ) = 0.0126582278 …   . {\displaystyle {\frac {1}{79}}=\sum _{n=1}^{\infty }{P(n)\times 10^{-(n+1)}}=0.0126582278\dots
Rydberg formula (1,892 words) [view diff] no match in snippet view article find links to article
atomic electron transition. Note: Here, n 2 > n 1 {\displaystyle n_{2}>n_{1}} By setting n 1 {\displaystyle n_{1}} to 1 and letting n 2 {\displaystyle n_{2}}
79 (number) (535 words) [view diff] exact match in snippet view article
1 79 = ∑ n = 1 ∞ P ( n ) × 10 − ( n + 1 ) = 0.0126582278 …   . {\displaystyle {\frac {1}{79}}=\sum _{n=1}^{\infty }{P(n)\times 10^{-(n+1)}}=0.0126582278\dots
United States congressional apportionment (4,720 words) [view diff] exact match in snippet view article find links to article
A_{m+1}={\sqrt {\frac {m}{m+2}}}\ A_{m}} A n = n1 n + 1   A n1 {\displaystyle A_{n}={\sqrt {\frac {n-1}{n+1}}}\ A_{n-1}} where n is still the number of seats
Phased array (5,021 words) [view diff] no match in snippet view article find links to article
accordingly[page needed]: A F = ∑ n = 1 N I n 1 [ ∑ m = 1 M I m 1 e j ( m − 1 ) ( k d x sin ⁡ θ cos ⁡ ϕ + β x ) ] e j ( n1 ) ( k d y sin ⁡ θ sin ⁡ ϕ + β
Jensen's inequality (4,475 words) [view diff] no match in snippet view article find links to article
( 1 − λ n + 1 ) ∑ i = 1 n λ i 1 − λ n + 1 x i + λ n + 1 x n + 1 ) ≤ ( 1 − λ n + 1 ) φ ( ∑ i = 1 n λ i 1 − λ n + 1 x i ) + λ n + 1 φ ( x n + 1 ) . {\displaystyle
Pound sterling (14,537 words) [view diff] no match in snippet view article find links to article
from the original on 25 June 2015. Retrieved 28 February 2012. sterling, n.1 and adj. "Easterling theory". Sterling Judaica. Archived from the original
Marcus Aurelius (16,718 words) [view diff] no match in snippet view article find links to article
Press, 1995), 21 n. 1. Mark, Joshua. 'Marcus Aurelius: Plato's Philosopher King'. World History Encyclopedia. 8 May 2018. Francis, p. 21 n.1, citing Justin
Winchester (6,495 words) [view diff] no match in snippet view article find links to article
2005 and 2012 at the behest of Winchester City Council.(51°03′43″N 1°18′55″W / 51.062°N 1.31525°W / 51.062; -1.31525 (The Square)) Winchester has a variety
Fresnel equations (8,291 words) [view diff] no match in snippet view article find links to article
| n 1 cos ⁡ θ i − n 2 cos ⁡ θ t n 1 cos ⁡ θ i + n 2 cos ⁡ θ t | 2 = | n 1 cos ⁡ θ i − n 2 1 − ( n 1 n 2 sin ⁡ θ i ) 2 n 1 cos ⁡ θ i + n 2 1 − ( n 1 n
Mathematical fallacy (3,127 words) [view diff] no match in snippet view article find links to article
N + 1 horses of the same colour. Thus if any N horses are all the same colour, any N + 1 horses are the same colour. This is clearly true for N = 1 (i
Polygonal number (1,109 words) [view diff] exact match in snippet view article find links to article
{\begin{aligned}P(s,n+1)-P(s,n)&=(s-2)n+1\,,\\P(s+1,n)-P(s,n)&=T_{n-1}={\frac {n(n-1)}{2}}\,,\\P(s+k,n)-P(s,n)&=kT_{n-1}=k{\frac {n(n-1)}{2}}\,.\end{aligned}}}
President of Russia (4,998 words) [view diff] no match in snippet view article find links to article
Retrieved 22 July 2017. "Закон РФ о поправке к Конституции РФ от 14.03.2020 N 1-ФКЗ "О совершенствовании регулирования отдельных вопросов организации и функционирования
Fundamental theorem of algebra (7,720 words) [view diff] no match in snippet view article find links to article
combined; in other words, | z n | > | a n1 z n1 + ⋯ + a 0 | . {\displaystyle \left|z^{n}\right|>\left|a_{n-1}z^{n-1}+\cdots +a_{0}\right|.} When z traverses
Tyne and Wear (2,322 words) [view diff] no match in snippet view article find links to article
Wear at the English Heritage Archive Tyne and Wear at Curlie Portal:  North East England 54°58′26″N 1°36′48″W / 54.974°N 1.6132°W / 54.974; -1.6132
Oxford City F.C. (1,675 words) [view diff] no match in snippet view article find links to article
(51°44′38″N 1°15′28″W / 51.7438°N 1.2578°W / 51.7438; -1.2578), which was used from 1900 to 1988; and Cutteslowe Park (51°47′28″N 1°15′47″W / 51.7911°N 1.2631°W
Affine transformation (3,570 words) [view diff] exact match in snippet view article find links to article
M = [ y 1 ⋯ y n + 1 1 ⋯ 1 ] [ x 1 ⋯ x n + 1 1 ⋯ 1 ] − 1 . {\displaystyle M={\begin{bmatrix}\mathbf {y} _{1}&\cdots &\mathbf {y} _{n+1}\\1&\cdots
Compound interest (2,547 words) [view diff] no match in snippet view article find links to article
compounding basis, so that ( 1 + r 1 n 1 ) n 1 = ( 1 + r 2 n 2 ) n 2 {\displaystyle \left(1+{\frac {r_{1}}{n_{1}}}\right)^{n_{1}}=\left(1+{\frac {r_{2}}{n_{2}}}\right)^{n_{2}}}
A* search algorithm (4,743 words) [view diff] no match in snippet view article find links to article
function f ( n ) = g ( n ) + ( 1 + ε w ( n ) ) h ( n ) {\displaystyle f(n)=g(n)+(1+\varepsilon w(n))h(n)} , where w ( n ) = { 1 − d ( n ) N d ( n ) ≤ N
Large numbers (7,081 words) [view diff] exact match in snippet view article find links to article
value of k n + 1 {\displaystyle {k_{n+1}}} is increased by 1 and everything to the right of ( n + 1 ) k n + 1 {\displaystyle ({n+1})^{k_{n+1}}} is rewritten
8 (8,076 words) [view diff] exact match in snippet view article find links to article
"Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2) equal to n*(n+1)/2 and 0 + 1 + 2 + ... + n)". The On-Line Encyclopedia of Integer Sequences
Polynomial ring (8,165 words) [view diff] no match in snippet view article find links to article
X n α n = ∑ i ( ∑ ( α 1 , … , α n1 ) ∣ ( α 1 , … , α n1 , i ) ∈ I c α 1 , … , α n1 X 1 α 1 ⋯ X n1 α n1 ) X n i , {\displaystyle \sum _{(\alpha
Grade I listed buildings in West Yorkshire (148 words) [view diff] no match in snippet view article find links to article
Ilkley House 1906–08 12 December 2014 SE1085747608 53°55′28″N 1°50′10″W / 53.924495°N 1.83616°W / 53.924495; -1.83616 (Heathcote) 1133518 More images
Tensor product (8,642 words) [view diff] no match in snippet view article find links to article
K^{n}\to K^{n},} and thus linear maps ψ : P n1 → P n1 {\displaystyle \psi :\mathbb {P} ^{n-1}\to \mathbb {P} ^{n-1}} of projective spaces over K . {\displaystyle
Integer partition (3,398 words) [view diff] no match in snippet view article find links to article
p(n)} by the convergent series. p ( n ) = 1 π 2 ∑ k = 1 ∞ A k ( n ) k ⋅ d d n ( 1 n1 24 sinh ⁡ [ π k 2 3 ( n1 24 ) ] ) {\displaystyle p(n)={\frac
Pseudorandom number generator (3,312 words) [view diff] no match in snippet view article find links to article
function f : N 1 → R {\displaystyle f:\mathbb {N} _{1}\rightarrow \mathbb {R} } (where N 1 = { 1 , 2 , 3 , … } {\displaystyle \mathbb {N} _{1}=\left\{1,2
Repunit (3,371 words) [view diff] no match in snippet view article find links to article
+ b + b 2 + ⋯ + b n1 = b n1 b − 1 for  | b | ≥ 2 , n1. {\displaystyle R_{n}^{(b)}\equiv 1+b+b^{2}+\cdots +b^{n-1}={b^{n}-1 \over {b-1}}\qquad
Finite field (6,162 words) [view diff] no match in snippet view article find links to article
denote by n ⋅ x the sum of n copies of x. The least positive n such that n1 = 0 is the characteristic p of the field. This allows defining a multiplication
List of tallest structures in France (81 words) [view diff] no match in snippet view article find links to article
transmitter, central mast 350 m 1970 Guyed Mast Rosnay 46°42′47.49″N 1°14′42.22″E / 46.7131917°N 1.2450611°E / 46.7131917; 1.2450611 (HWU transmitter, central
Andorra la Vella (1,969 words) [view diff] no match in snippet view article find links to article
Andorra la Vella is located in the south west of Andorra, at 42°30′N 1°30′E / 42.500°N 1.500°E / 42.500; 1.500, at the confluence of two mountain streams
Nuclear fusion (9,987 words) [view diff] no match in snippet view article find links to article
times the product of the reactant number densities: f = n 1 n 2 ⟨ σ v ⟩ . {\displaystyle f=n_{1}n_{2}\langle \sigma v\rangle .} If a species of nuclei
Discrete space (2,287 words) [view diff] no match in snippet view article find links to article
satisfies this inequality: 2 − ( n + 1 ) < r 1 < 2 n + 1 r r − 1 < 2 n + 1 log 2 ⁡ ( r − 1 ) < n + 1 − log 2 ⁡ ( r ) < n + 1 − 1 − log 2 ⁡ ( r ) < n {\displaystyle
Grade II* listed buildings in the West Midlands (142 words) [view diff] no match in snippet view article find links to article
Anglican Church 1907-1909 26 August 1976 SP1091698740 52°35′11″N 1°50′25″W / 52.586358°N 1.840316°W / 52.586358; -1.840316 (All Saints Church) 1343304
APICA (synthetic cannabinoid drug) (601 words) [view diff] no match in snippet view article
APICA (2NE1, SDB-001, N-(1-adamantyl)-1-pentyl-1H-indole-3-carboxamide) is an indole based drug that acts as a potent agonist for the cannabinoid receptors
Complex number (13,683 words) [view diff] no match in snippet view article find links to article
contrary to the case of positive real numbers, one has ( z n ) 1 / n ≠ z , {\displaystyle (z^{n})^{1/n}\neq z,} since the left-hand side consists of n values
Sheffield (20,666 words) [view diff] no match in snippet view article find links to article
first time in its history. Sheffield is located at 53°22′59″N 1°27′57″W / 53.38297°N 1.4659°W / 53.38297; -1.4659. It lies directly beside Rotherham
Adjugate matrix (4,805 words) [view diff] no match in snippet view article find links to article
R. The (i, j)-minor of A, denoted Mij, is the determinant of the (n − 1) × (n − 1) matrix that results from deleting row i and column j of A. The cofactor
Lindisfarne (8,986 words) [view diff] no match in snippet view article find links to article
Lighthouse Location Old Law, Middleton, United Kingdom Coordinates 55°42′N 1°48′W / 55.7°N 1.8°W / 55.7; -1.8 Tower Constructed 1859  Designed by John Dobson 
Abelian group (5,288 words) [view diff] no match in snippet view article find links to article
Aut ⁡ ( P ) | = ( p n1 ) ⋯ ( p n − p n1 ) . {\displaystyle \left|\operatorname {Aut} (P)\right|=(p^{n}-1)\cdots (p^{n}-p^{n-1}).} In the most general
Mid Suffolk (982 words) [view diff] no match in snippet view article find links to article
52°09′22″N 1°02′56″E / 52.1560°N 1.0489°E / 52.1560; 1.0489 Mid Suffolk is a local government district in Suffolk, England. The district is primarily
Grade I listed buildings in Nottinghamshire (153 words) [view diff] no match in snippet view article find links to article
Parish Church 12th century 13 October 1966 SK5034952363 53°03′58″N 1°15′00″W / 53.066144°N 1.250077°W / 53.066144; -1.250077 (Ruins of Church of All Saints)
List of Sites of Special Scientific Interest in Oxfordshire (5,116 words) [view diff] no match in snippet view article find links to article
Nature Conservation Review. Vol. 2. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-21403-2. 51°45′N 1°17′W / 51.75°N 1.28°W / 51.75; -1.28
Honeycomb (geometry) (1,319 words) [view diff] no match in snippet view article
A ~ n1 {\displaystyle {\tilde {A}}_{n-1}} C ~ n1 {\displaystyle {\tilde {C}}_{n-1}} B ~ n1 {\displaystyle {\tilde {B}}_{n-1}} D ~ n1 {\displaystyle
List of Sites of Special Scientific Interest in Berkshire (4,124 words) [view diff] no match in snippet view article find links to article
51°25′N 1°00′W / 51.417°N 1.000°W / 51.417; -1.000 In England, Sites of Special Scientific Interest (SSSIs) are designated by Natural England, which
Cotswold Way (935 words) [view diff] no match in snippet view article find links to article
Castle 51°56′49″N 1°57′22″W / 51.947°N 1.956°W / 51.947; -1.956 (Sudeley Castle) SP031276 Sudeley Castle 51°57′25″N 1°58′08″W / 51.957°N 1.969°W / 51
Degree (graph theory) (1,274 words) [view diff] no match in snippet view article
regular graph where all vertices have the maximum possible degree, n1 {\displaystyle n-1} . In a signed graph, the number of positive edges connected to
Simulated annealing (4,573 words) [view diff] no match in snippet view article find links to article
neighbors of each vertex is ∑ k = 1 n1 k = n ( n1 ) 2 = 190 {\displaystyle \sum _{k=1}^{n-1}k={\frac {n(n-1)}{2}}=190} edges (coming from n choose
Errors and residuals (2,168 words) [view diff] no match in snippet view article find links to article
only n − 1 degrees of freedom: 1 σ 2 ∑ i = 1 n r i 2 ∼ χ n1 2 . {\displaystyle {\frac {1}{\sigma ^{2}}}\sum _{i=1}^{n}r_{i}^{2}\sim \chi _{n-1}^{2}
Ionization energy (5,892 words) [view diff] no match in snippet view article find links to article
most loosely bound electron from the species having a positive charge of (n1). For example, the first three ionization energies are defined as follows:
M27 motorway (1,297 words) [view diff] no match in snippet view article find links to article
Constructed 1972–83 Major junctions West end Cadnam 50°55′06″N 1°35′35″W / 50.9182°N 1.5930°W / 50.9182; -1.5930 (M27 motorway (western end)) Major