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Longer titles found: Gaussian binomial coefficient (view), Central binomial coefficient (view)

searching for Binomial coefficient 35 found (262 total)

Q-Vandermonde identity (859 words) [view diff] exact match in snippet view article find links to article

applications to quantum groups, a different q-binomial coefficient is used. This q-binomial coefficient, which we denote here by B q ( n , k ) {\displaystyle

Entropy (information theory) (10,194 words) [view diff] no match in snippet view article

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential

35 (number) (475 words) [view diff] exact match in snippet view article

Sequences. OEIS Foundation. Retrieved 2016-05-31. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia

15 (number) (1,053 words) [view diff] exact match in snippet view article

Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A000332 (Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24)". The On-Line Encyclopedia

Bijective proof (400 words) [view diff] exact match in snippet view article find links to article

cream cones. Problems that admit bijective proofs are not limited to binomial coefficient identities. As the complexity of the problem increases, a bijective

P-adic analysis (1,043 words) [view diff] exact match in snippet view article find links to article

{x \choose k}={\frac {x(x-1)(x-2)\cdots (x-k+1)}{k!}}} is the kth binomial coefficient polynomial. Over the field of real numbers, the assumption that the

Gosper's algorithm (582 words) [view diff] exact match in snippet view article find links to article

from the original on 2019-04-12. Retrieved 2020-01-10. algorithm / binomial coefficient identities / closed form / symbolic computation / linear recurrences

Theta divisor (492 words) [view diff] exact match in snippet view article find links to article

if h0(O(D)) = r + 1, the multiplicity of Wk at class(D) is the binomial coefficient ( g − k + r r ) . {\displaystyle {g-k+r \choose r}.} When k = g −

Sierpiński triangle (2,723 words) [view diff] exact match in snippet view article find links to article

Sierpiński triangle obtained by shading the first 25 (32) levels of a Pascal's triangle white if the binomial coefficient is even and black otherwise

John Selfridge (1,583 words) [view diff] exact match in snippet view article find links to article

Selfridge, J. L. (1993). "Estimates of the least prime factor of a binomial coefficient". Math. Comput. 61 (203): 215–224. Bibcode:1993MaCom..61..215E. doi:10

Artin–Hasse exponential (1,067 words) [view diff] exact match in snippet view article find links to article

expansion of (1 - xn)a are p-integral by p-adic continuity of the binomial coefficient polynomials t(t-1)...(t-k+1)/k! in t together with their obvious

Q-derivative (1,782 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\binom {n}{k}}_{q}} is the q {\displaystyle q} -binomial coefficient. By changing the order of summation as r = n − k {\displaystyle r=n-k}

1001 (number) (717 words) [view diff] exact match in snippet view article

in The Book of One Thousand and One Nights. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia

Latin letters used in mathematics, science, and engineering (4,250 words) [view diff] exact match in snippet view article find links to article

electrical theory with indices denoting the number of combinations, a binomial coefficient together with a degree symbol (°), the Celsius measurement of temperature

Möbius function (3,119 words) [view diff] exact match in snippet view article find links to article

\mu _{k}\left(p^{a}\right)=(-1)^{a}{\binom {k}{a}}\ } where the binomial coefficient is taken to be zero if a > k {\displaystyle a>k} . The definition

Binomial transform (2,433 words) [view diff] exact match in snippet view article find links to article

d ) ) {\displaystyle {\binom {\nu _{p}(n)}{\nu _{p}(d)}}} is the binomial coefficient. This convolution appears in the book by P. J. McCarthy (1986) and

Tensor algebra (4,161 words) [view diff] exact match in snippet view article find links to article

{\displaystyle v_{i}\cdot v_{j}=(i,j)v_{i+j}} where (i,j) denotes the binomial coefficient for ( i + j i ) {\displaystyle {\tbinom {i+j}{i}}} . This bialgebra

Beam splitter (4,851 words) [view diff] exact match in snippet view article find links to article

{\displaystyle M=n+m-N} and the ( n j ) {\displaystyle {\tbinom {n}{j}}} is a binomial coefficient and it is to be understood that the coefficient is zero if j ∉ {

Cofree coalgebra (1,708 words) [view diff] exact match in snippet view article find links to article

{\displaystyle v_{i}\cdot v_{j}=(i,j)v_{i+j}} where (i,j) denotes the binomial coefficient ( i + j i ) {\displaystyle {\tbinom {i+j}{i}}} . This bialgebra is

Stanley sequence (1,140 words) [view diff] exact match in snippet view article find links to article

n {\displaystyle n} such that the n {\displaystyle n} th central binomial coefficient is 1 mod 3, and the numbers whose balanced ternary representation

List of inventions in the medieval Islamic world (9,274 words) [view diff] exact match in snippet view article find links to article

theorem: The first formulation of the binomial theorem and the table of binomial coefficient can be found in a work by Al-Karaji, quoted by Al-Samaw'al in his

Indian mathematics (13,924 words) [view diff] case mismatch in snippet view article find links to article

1007/1-4020-2321-9_7, ISBN 978-1-4020-2320-0. Fowler, David (1996), "Binomial Coefficient Function", The American Mathematical Monthly, 103 (1): 1–17, doi:10

Harmonic number (5,594 words) [view diff] case mismatch in snippet view article find links to article

359–378. doi:10.1016/s0196-8858(03)00016-2. Wenchang Chu (2004). "A Binomial Coefficient Identity Associated with Beukers' Conjecture on Apery Numbers" (PDF)

List of unsolved problems in mathematics (19,901 words) [view diff] exact match in snippet view article find links to article

(1971). "Research Problems: How often does an integer occur as a binomial coefficient?". American Mathematical Monthly. 78 (4): 385–386. doi:10.2307/2316907

Timeline of scientific discoveries (10,600 words) [view diff] exact match in snippet view article find links to article

integer logarithm. 850: Mahāvīra derives the expression for the binomial coefficient in terms of factorials, ( n r ) = n ! r ! ( n − r ) ! {\displaystyle

Caputo fractional derivative (2,321 words) [view diff] exact match in snippet view article find links to article

\left(a+1\right)}{\Gamma \left(b+1\right)\cdot \Gamma \left(a-b+1\right)}}} is the binomial coefficient. Caputo-type fractional derivative is closely related to the Riemann–Liouville

Lifting-the-exponent lemma (2,091 words) [view diff] exact match in snippet view article find links to article

cannot be directly applied when p = 2 {\displaystyle p=2} because the binomial coefficient ( p 2 ) = p ( p − 1 ) 2 {\displaystyle {\binom {p}{2}}={\frac {p(p-1)}{2}}}

1000 (number) (24,094 words) [view diff] exact match in snippet view article

Encyclopedia of Integer Sequences. OEIS Foundation. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia

Super-resolution optical fluctuation imaging (2,242 words) [view diff] exact match in snippet view article find links to article

represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating

Distribution (mathematics) (21,631 words) [view diff] exact match in snippet view article

α {\displaystyle \beta \geq \alpha } we define their multi-index binomial coefficient as: ( β α ) := ( β 1 α 1 ) ⋯ ( β n α n ) . {\displaystyle {\binom

Pascal's pyramid (3,339 words) [view diff] exact match in snippet view article find links to article

examples in 3 and 2 dimensions, respectively. ^2 The formula for the binomial coefficient is usually expressed as ⁠n!/x!(n−x)!⁠, where n−x = y. Arbitrary layer

Smoothstep (2,454 words) [view diff] exact match in snippet view article find links to article

1, N - n) * Math.pow(x, N + n + 1); return result; } // Returns binomial coefficient without explicit use of factorials, // which can't be used with negative

Nome (mathematics) (13,956 words) [view diff] exact match in snippet view article

Index n Central binomial coefficient square [ ( 2 n − 2 ) ! ] 2 [ ( n − 1 ) ! ] 4 {\displaystyle {\frac {[(2n-2)!]^{2}}{[(n-1)!]^{4}}}} Sequence number

Generating function transformation (11,140 words) [view diff] exact match in snippet view article find links to article

parameter x {\displaystyle x} . These relations also still hold if the binomial coefficient substitution of ( n k ) ⟼ ( n + p k + p ) {\displaystyle {\binom

Spaces of test functions and distributions (18,992 words) [view diff] exact match in snippet view article find links to article

α {\displaystyle \beta \geq \alpha } we define their multi-index binomial coefficient as: ( β α ) := ( β 1 α 1 ) ⋯ ( β n α n ) . {\displaystyle {\binom