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alternate case: constant term

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b} , and c {\displaystyle c} . A constant coefficient, also known as constant term or simply constant, is a quantity either implicitly attached to the

};q)_{\infty }}.} ⟨ f , g ⟩ = ( constant term of  f g ¯ Δ ) / | W | {\displaystyle \langle f,g\rangle =({\text{constant term of }}f{\overline {g}}\Delta )/|W|}

from the solution of the homogeneous equation obtained by removing the constant term. The term homogeneous was first applied to differential equations by

This article is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Unless otherwise stated, all

where the only term in the stress–energy tensor is the cosmological constant term (and thus, the lambdavacuums can be taken as cosmological models). More

the Dyson conjecture (Freeman Dyson 1962) is a conjecture about the constant term of certain Laurent polynomials, proved independently in 1962 by Wilson

of polynomials in F[X] with constant term in R. This ring is not Noetherian, since an element like X with zero constant term can be divided indefinitely

associated to an affine Weyl group, and can be used to prove Macdonald's constant term conjecture for Macdonald polynomials. Let V {\displaystyle V} be a Euclidean

only defined if the series g being substituted has zero constant term (if not, the constant term of the result would be given by an infinite series with

the recurrence for binary search but has a larger S(n) term than the constant term of binary search. In prune and search algorithms S(n) is typically at

in which the only term in the stress–energy tensor is a cosmological constant term. This can be interpreted physically as a kind of classical approximation

In mathematics, the classical Kronecker limit formula describes the constant term at s = 1 of a real analytic Eisenstein series (or Epstein zeta function)

groups (blocks), for each of which the model will have a different constant term, in such a way that the block constants will be uncorrelated with the

They were introduced by Cherednik, who used them to prove Macdonald's constant term conjecture for Macdonald polynomials. Infinitesimal Cherednik algebras

sends each polynomial to its constant term. It maps a polynomial to zero if and only if said polynomial's constant term is 0. If we instead work with

introduced double affine Hecke algebras, and used them to prove Macdonald's constant term conjecture in (Cherednik 1995). He has also dealt with algebraic geometry

the exponent e can be set arbitrarily close to 1 by increasing k, the constant term in the function grows very rapidly. The growth rate for mixed-level

" Algorithm:"Let the square of the square of product as 'shi' (the constant term), and let the square of the long side of right angle triangle be the

p1(x) + p2(x) + ... + pn(x). The constant term of P(x) is in fact the sum of all the votes, because the constant term of P(x) is the sum of the constant

called the constant term of the equation (by analogy with algebraic equations), even when this term is a non-constant function. If the constant term is the

comes from so-called dark energy, which accounts for the cosmological constant term. Although the total density is equal to the critical density (exactly

f(a) = 0. Then f has a Taylor series at a and its constant term is zero. Because this constant term is zero, the function f(x) / (x − a) will have a Taylor

In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle

equations in n variables over a field F. Assume that the equations all have constant term zero, so that (0, 0, ... ,0) is a common solution. We say that F is

residual values is equal to zero whenever the model function contains a constant term. Left-multiply the expression for the residuals by XT WT: X T W r ^

the action of G, there is a G-invariant polynomial F on V, without constant term, such that F(v) ≠ 0. The polynomial can be taken to be homogeneous,

(generalized) pentagonal numbers (sequence A001318 in the OEIS). (The constant term 1 corresponds to k = 0 {\displaystyle k=0} .) This holds as an identity

n matrices. This equation is homogeneous because there is no vector constant term added to the end of the equation. The same equation might also be written

used as an estimator for r. Just like a unit root test, there can be a constant term, a trend term, both, or neither in the model. For a general VAR(p) model:

exponential map from G to the group of the power series in R[[t]] with constant term 1. In other words the functor Exp from abelian groups to commutative

asymptotic to ⁠−+1/12⁠ + CN2, where C is a constant that depends on f. The constant term of the asymptotic expansion does not depend on f: it is necessarily

the Laplace–Beltrami operator which has Fourier expansion with zero constant term.) The zeta-function also has a zero at every pole of the determinant

different system solutions. A first-order matrix difference equation with constant term can be written as y t + 1 = A y t + c , {\displaystyle \mathbf {y} _{t+1}=A\mathbf

slope-intercept form as f ( x ) = a + b x {\displaystyle f(x)=a+bx} , the constant term a {\displaystyle a} is the y {\displaystyle y} -coordinate of the y

modular function is T 2 A ( τ ) {\displaystyle T_{2A}(\tau )} , with constant term a ( 0 ) = 104 {\displaystyle a(0)=104} : j 2 A ( τ ) = T 2 A ( τ ) +

dependent term is used to calculate core-core potentials rather than the constant term. AM1* parameters are now available for H, C, N, O, F, Al, Si, P, S,

quantum angular momentum squared operator, but it further contains a constant term ⁠3ħ2/2⁠. (This extra term offset is pedagogically significant, since

{\displaystyle p} : price index k {\displaystyle k} : constant term l {\displaystyle l} : constant term y d {\displaystyle y^{d}} : demand for domestic output

g(x)=(x-1)(x-2)\cdots (x-(p-1)).} g has degree p − 1, leading term xp − 1, and constant term (p − 1)!. Its p − 1 roots are 1, 2, ..., p − 1. Now consider h ( x )

{\mathbf {Q} }}[[T]]} consisting of those formal power series whose constant term is rational. Bouvier, Alain; Kabbaj, Salah (1988). "Examples of Jaffard

d to Siegel modular forms of degree d − 1, generalizing taking the constant term of a modular form. The kernel is the space of Siegel cusp forms of degree d

{\displaystyle f} from its leading coefficient a n {\displaystyle a_{n}} and constant term a 0 {\displaystyle a_{0}} . (See Rational Root Theorem.) Use the factor

twelfth triangular number 78. Meanwhile, their sum is 41, which is the constant term in Euler's lucky numbers that yield prime numbers of the form k2 − k

applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero (without which it would be divisible by x anyway). This is

Sarnak 1991). The Smith–Minkowski–Siegel mass formula is essentially the constant term of the Weil–Siegel formula. If f is an n-dimensional positive definite

(PDF). Proceedings of the Journées. p. 44. Average distance over times. Constant term in VSOP87. It corresponds to the average taken of many short, equal

unknown x, so the numerals on that line mean 18x. The line below is the constant term (-316) and the line above is the coefficient of the quadratic (x2) term

The additional freight charges, discounts or premiums incurred. This constant term is determined through contract negotiations. The Japan Crude Cocktail

{\displaystyle f'(x)} Integral ∫ f ( x ) d x {\displaystyle \int f(x)dx} (constant term is omitted) Multiplicative derivative f ∗ ( x ) {\displaystyle f^{*}(x)}

any integer-valued polynomials P1,..., Pk in one unknown m all with constant term 0, there are infinitely many integers x, m such that x + P1(m), ...

derivative of the two sides are equal and that both sides have the same constant term. In a similar way, one can verify a product expansion for the Artin–Hasse

A linear matrix difference equation of the homogeneous (having no constant term) form X t + 1 = A X t {\displaystyle X_{t+1}=AX_{t}} has closed form

upon taking the derivative of velocity, because the derivative of a constant term is zero. This same pattern applies to further integrations and derivatives

by a set {x} is the ring of all integral polynomials over x with no constant term, while the free ring generated by {x} is just the polynomial ring Z[x]

mathématiciens (1970, Nice). Vol. 2. pp. 331–335. Macdonald, I. G. (1998). "Constant term polynomials, orthogonal polynomials, and affine Hecke algebras". Doc

i} -th observations on all the explanatory variables. Typically, a constant term is included in the set of regressors X {\displaystyle \mathbf {X} }

sixty-three, σ ( 63 ) = 104 {\displaystyle \sigma (63)=104} , is equal to the constant term a ( 0 ) = 104 {\displaystyle a(0)=104} that belongs to the principal

p. 1. Standish and Williams(2012) p 27 Average distance over times. Constant term in VSOP87. It corresponds to the average taken of many short, equal

manipulation. The above form is sometimes called the standard form. If the constant term is put on the left, the equation becomes a x + b y − c = 0 , {\displaystyle

{\displaystyle Z={\frac {D^{2}}{2\lambda }}-{\frac {\lambda }{8}}} The constant term λ 8 {\displaystyle {\frac {\lambda }{8}}} can be neglected. In antenna

unknown x, so the numerals on that line mean 18x. The line below is the constant term (-316) and the line above is the coefficient of the quadratic (x2) term

reached, at the end of the segment corresponding to the equation's constant term, is the terminus. A line is then launched from the origin at some angle

+a_{n}x_{n}+b=0.} The coefficient b, often denoted a0 is called the constant term (sometimes the absolute term in old books). Depending on the context

lambda dust (which models a dust with a carefully chosen cosmological constant term) the Tipler cylinder (a cylindrically symmetric metric with CTCs) Bonnor-Steadman

up to ἴσ M {\displaystyle \mathrm {M} } the zeroth power (that is, a constant term) ζ {\displaystyle \zeta } the unknown quantity (because a number x {\displaystyle

determinant of supply is caused by a change in the y-intercept, the constant term of the supply equation. The supply curve shifts up and down the y axis

{4}-1408x^{3}+3124x^{2}+10001){\Big )}+C.\end{aligned}}} But if the constant term 71 is changed to 72, it is not possible to represent the antiderivative

g=G{\frac {M_{\oplus }}{r_{\oplus }^{2}}}.} The gravitational constant is a constant term in the Einstein field equations of general relativity, G μ ν + Λ g μ

the special case of the multiplication where p = p0 is reduced to its constant term (the term that is independent of X); that is p 0 ( q 0 + q 1 X + ⋯ +

polynomial (interpreting the resulting powers as matrix powers, and the constant term c {\displaystyle c} as c {\displaystyle c} times the identity matrix)

  (A) Hiroo Kanamori used W0 in place of Es (dyn.cm) and consider a constant term (W0/Mo = 5 × 10−5) in Eq. (A) and estimated Ms and denoted as Mw (dyn

Dark energy in its simplest formulation is modeled by a cosmological constant term in Einstein field equations of general relativity, but its composition

(1987). "The Coeffecient of Determination for Regression without a Constant Term". In Heijmans, Risto; Neudecker, Heinz (eds.). The Practice of Econometrics

_{k=0}^{N}b_{k}t^{k}{\biggr )}=\sum _{k=0}^{N}a_{k}b_{k}.} Putting t=τ−1, this is the constant term in the product of two formal Laurent series. Thus, given a polynomial

but varying the lowest-order constant term. Bk(x; C) is the same function as above, but with the lowest-order constant term replaced by a parameter C: p

{\displaystyle {\widehat {\alpha \,}}} is the estimated value of the constant term α {\displaystyle \alpha } and β ^ {\displaystyle {\widehat {\beta \

latter case, integrating the differential equation above leads to a constant term for the current, that represents a fixed DC bias flowing through the

machine could be fed two linear equations with up to 29 variables and a constant term and eliminate one of the variables. This process would be repeated manually

+b_{1})z^{-1}}{(a_{0}K+a_{1})+(-a_{0}K+a_{1})z^{-1}}}} Normally the constant term in the denominator must be normalized to 1 before deriving the corresponding

about 5.5 mm (0.22 in) to the total height. This can be treated like a constant term which can be added to adapt traditional scope height equations for the

field of characteristic p: any inseparable polynomial f(Xp) without constant term satisfies the condition since all derivatives are zero. Another counterexample

the coefficient corresponding to the highest degree to one, and the constant term to zero. Therefore, p + q − 2 {\displaystyle p+q-2} known distinct p

solution to the field equations of General Relativity with a cosmological constant term, the Schwarzschild-De Sitter spacetime, arises as a specific case of

in energy is what we measure and not the absolute value of it, the constant term ⁠1/2⁠ħωq can be ignored without changing the equations of motion. Hence

because ⁠ a {\displaystyle a} ⁠ is non-zero. Afterwards, we subtract the constant term ⁠ c / a {\displaystyle c/a} ⁠ to isolate it on the right-hand side:

Divide each side by a, the coefficient of the squared term. Subtract the constant term c/a from both sides. Add the square of one-half of b/a, the coefficient

the ordinary polynomial in g while C N {\displaystyle C_{N}} is the constant term. The period n {\displaystyle n} is usually given in years, but the calculation

{\omega _{c}}} Note that the error in this case is only about 2%, for the constant term, and using the second term, ( 1 − ω c 2 2 ω 2 ) {\displaystyle \left(1-{\frac

which does not have a root at 0 (that is a polynomial with a nonzero constant term) then the minimum number of nonreal roots is equal to n − ( p + q )

X, Y, and Z, with zi having been augmented with a 1 to allow for a constant term in the regression. Solving the linear regression problem amounts to

integer is again an integer, because it is equal (up to sign) to the constant term of the characteristic polynomial. In algebraic number theory one defines

r-1} is a result of failing to allow for the additional effect of the constant term in many regressions. That the result based on r − 1 {\textstyle r-1}

autoregressive integrated moving average (ARIMA) (0,1,1) model with no constant term. The time constant of an exponential moving average is the amount of

real interest rate r* = long-run target for the real interest rate g = constant term (or the slope of the MPRF) π = actual inflation rate π* = long-run target

Consider the submodule K consisting of all those polynomials with zero constant term. Since every polynomial contains only finitely many terms whose coefficients

degree of the denominator. For fitting rational function models, the constant term in the denominator is usually set to 1. Rational functions are typically

{x} -\mathbf {x} _{0}\right\|_{Q}^{2}} or, equivalently up to a constant term, x T ( A + Q ) x − 2 x T ( b + Q x 0 ) . {\displaystyle \mathbf {x}

section § Alternatives to dark energy). The "cosmological constant" is a constant term that can be added to Einstein field equations of general relativity

general form of the Einstein field equations included a cosmological constant term. The jury awarded Lemaître a prize of 8,000 Belgian francs. Cardinal

However, he realized that his equations permitted the introduction of a constant term which could counteract the attractive force of gravity on the cosmic

A solution of O ( N 2 ) {\displaystyle O(N^{2})} with a reasonable constant term would be disastrous. On the other hand, a solution that is Ω ( N 4 )

{\displaystyle P_{1},\ldots ,P_{k}} in one unknown m {\displaystyle m} all with constant term 0, there are infinitely many integers x , m {\displaystyle x,m} such

quantum angular momentum squared operator, but it further contains a constant term 3ħ2/2. (This extra term is actually physically significant, since it

equation it is convenient to convert it to homogeneous form, with no constant term. This is done by first finding the equation's steady state value—a value

Logistic regression can account for stratification by having a different constant term for each stratum. Let us denote Y i ℓ ∈ { 0 , 1 } {\displaystyle Y_{i\ell

coefficients, in m variables of order at most k and with zero as the constant term. This is a real vector space with dimension dim ⁡ { R k [ x 1 , … ,

dynamic cosmology of Alexander Friedmann. Removing the cosmological constant term from the Friedmann equations on the grounds that it was both unsatisfactory

negative-power terms. For example, the Laurent series consisting only of the constant term 1 is identified with the real number 1, and the series with only the

bijection between the set of elements of S with constant term 0 and the set of elements of S with constant term 1; the inverse of exp is log r = exp ⁡ ( s

2.38 ⋅ | G | ) {\displaystyle O(n^{2.38}\cdot |G|)} . However, the constant term hidden by the Big O Notation is so large that the Coppersmith–Winograd

third equation is linearly dependent on the first two. Note that if the constant term in the original third equation had been anything other than –7, the

calculation becomes nontrivial, because the sums are very long; the constant term is the determinant, which for an n × n {\displaystyle n\times n} matrix

a polynomial, if it exists, must be the quotient of a factor of the constant term and a factor of the leading coefficient. In the case of p ( x ) = x

power (exponent)   2 – coefficient   3 – term   4 – operator   5 – constant term   c {\displaystyle c} – constant   x {\displaystyle x} y {\displaystyle

coefficients of the quadratic and a 0 {\displaystyle a_{0}} be the constant term. Similarly, let r 1 , r 2 {\displaystyle {r_{1}},{r_{2}}} be the roots

axes, as is the determinant of the 3 × 3 matrix above.: pp. 60–62  The constant term F and the sum D2 + E2 are invariant under rotation only.: pp. 60–62 

coordinates of the final coordinate system (i.e. the center of mass). This constant term does not affect the dynamics of the gyroscope and it can be neglected

t = ε t {\displaystyle \phi (B)X_{t}=\varepsilon _{t}\,} (where the constant term has been suppressed by assuming that the variable has been measured

\ell } and r {\displaystyle r} are the same as above; note the changed constant term now 1, from 0.75 above. For example, a single conductor of a lamp cord

hazards are proportional. Often there is an intercept term (also called a constant term or bias term) used in regression models. The Cox model lacks one because

{\displaystyle p_{\mathbf {A} }(\mathbf {A} )=\mathbf {0} .} Separating the constant term and multiplying the equation by adj(A) gives an expression for the adjugate

is T 2 A ( τ ) {\displaystyle T_{2A}(\tau )} where one can set the constant term a(0) = 104. j 2 A ( τ ) = T 2 A ( τ ) + 104 = ( ( η ( τ ) η ( 2 τ )

this solution, as the point varies, by a formal power series in t. The constant term is 1 and the higher coefficients are functions determined recursively

the eigenvalues. Similarly, the determinant is – up to the sign – the constant term of the characteristic polynomial, i.e. the value of en. Thus the determinant

rule that does not require any inputs is one that states the type of a constant term. For example, to assert that there is a term 0 {\displaystyle 0} of

then, by referring back to the original inequality, we have that the constant term is zero. The theorem can also be used to deduce that the domain of a

regularization. If s = 0 is an isolated singularity, the sum is defined by the constant term of the Laurent series expansion. If the series f ( s ) = 1 a 1 s + 1

infinity, as opposed to the entire real line. By such a changing of constant term in the effective potential, the results obtained by WKB approximation

corresponds to a non-trivial zero of the Riemann zeta-function. The constant term of the pole at s = 1 is described by the Kronecker limit formula. The

are real (as can be seen from Descartes' rule of signs) unless the constant term is also zero. Samuelson, Paul (1968). "How Deviant Can You Be?". Journal

is T 5 A ( τ ) {\displaystyle T_{5A}(\tau )} where one can set the constant term a(0) = −6 (OEIS: A007251), j 5 A ( τ ) = T 5 A ( τ ) − 6 = ( η ( τ )

resulting in perfect correlation between the dummy variables and the constant term. Multicollinearity (as long as it is not "perfect") can be present resulting

power (exponent)   2 – coefficient   3 – term   4 – operator   5 – constant term   c {\displaystyle c} – constant   x {\displaystyle x} y {\displaystyle

of adding to it. Additionally, urban households usually have a high constant term and a low slope. This shows that simply reducing mortality may not result

{(\ln k)^{n}}{k}}\right)-{\frac {(\ln m)^{n+1}}{n+1}}\right)}.} The constant term γ0 is the Euler–Mascheroni constant. For all s ∈ ℂ, s ≠ 1, the integral

is T 7 A ( τ ) {\displaystyle T_{7A}(\tau )} where one can set the constant term a(0) = 10 (OEIS: A007264), j 7 A ( τ ) = T 7 A ( τ ) + 10 = ( ( η (

definition is formal, the exponential of this power series without constant term denotes the usual development. see for example Silverman, Joseph H.

{1}{\det(CZ+D)^{k}}}} Sometimes the series is multiplied by a constant so that the constant term of the Fourier expansion is 1. Here Z is an element of the Siegel upper

by its characteristic power series Q(z), and every power series with constant term 1 gives rise to a multiplicative sequence. To recover a multiplicative

formal power series, then J(R) consists of those power series whose constant term is zero, i.e. the power series in the ideal (X1, ..., Xn). In the case

rx^{2}+sy^{2}+tz^{2}+2uyz+2vzx+2wxy=0.} It has no linear terms and no constant term. The equation of a circle of radius r having center at actual-distance

Faddeev–LeVerrier algorithm. That is, for generic n, detA = (−1)nc0 the signed constant term of the characteristic polynomial, determined recursively from c n =

^{\mu }\theta )(\partial _{\mu }\theta )-m^{2}v^{2}~.} Note that the constant term m 2 v 2 {\displaystyle m^{2}v^{2}} in the Lagrangian density has no

{\displaystyle x^{2}} term is also zero, and hence the leading non-constant term is of order x 4 {\displaystyle x^{4}} . The inflection point for a simple

convergent in y {\textstyle y} in a neighborhood of zero. To find the constant term of C ( x , y ) {\textstyle C(x,y)} , simply calculate the coefficient

terms of the other equations does not replicate the one equation's constant term. Example with one solution: 2x = 2, x = 1. Example with no solution:

case of polynomials, another formula for the tangent has a simpler constant term and is more symmetric: x p x ′ ( a , b ) + y p y ′ ( a , b ) + p ∞ ′

∈ { 2 , … , n } , {\displaystyle i,j\in \{2,\dotsc ,n\},} where the constant term n − 1 {\displaystyle n-1} provides sufficient slack that x i j = 0 {\displaystyle

derivative of that: p = 5,028.796195 + 2.2108696 T + higher order terms. The constant term of this speed (5,028.796195 arcseconds per century in above equation)

Materials. Addison-Wesley Publishing Company. p. 214. An arbitrary constant term is ignored. The lowest-order term in the energy can be written in more

shares can be renewed. The dealer generates a new random polynomial with constant term zero and calculates for each remaining player a new ordered pair, where

domain. The ring Z+XQ[X] of all rational polynomials with integral constant term is an example of an integral domain (actually a GCD domain) that does

polynomials are also irreducible. A primitive polynomial must have a non-zero constant term, for otherwise it will be divisible by x. Over GF(2), x + 1 is a primitive

p-adic factorization has factors in Zp. Consequently, the norm term (constant term) for each factor is a p-adic integer, and one of these is the integer

and k is the index of the first non-zero coefficient following the constant term. For z sufficiently close to z0 this function has behavior asymptotically

H_{u}H_{d}+y_{u}H_{u}QU^{c}+y_{d}H_{d}QD^{c}+y_{l}H_{d}LE^{c}} The constant term is unphysical in global supersymmetry (as opposed to supergravity).

two roots are a pair of complex conjugates, whose product is 1 (the constant term of the quadratic), and whose sum is 2 cos θ (the negated linear term)

is T 3 A ( τ ) {\displaystyle T_{3A}(\tau )} where one can set the constant term a(0) = 42 (OEIS: A030197), j 3 A ( τ ) = T 3 A ( τ ) + 42 = ( ( η (

xd(Q(x) − Q(⁠1/x⁠)), where Q is a monic polynomial of degree d with no constant term. If an antipalindromic polynomial P has even degree 2n over a field

calculus on manifolds. Of key interest is the Laplacian, and, with a constant term, what amounts to the Klein–Gordon operator. Cotangent bundles, by their

convolution by taking the coefficient vectors for a(x) and b(x) with constant term first, then appending zeros so that the resultant coefficient vectors

t − 1 + c + e t {\displaystyle y_{t}=y_{t-1}+c+e_{t}} where c is a constant term referred to as the "drift" term, and e t {\displaystyle e_{t}} is white

power series over the same ring as the formal groups which has zero constant term and is such that: f ( F ( X , Y ) ) = G ( f ( X ) , f ( Y ) ) {\displaystyle

=\left({\frac {\eta (q)}{\eta (q^{2})}}\right)^{24}} is (up to the constant term) the McKay–Thompson series for the class 2B of the Monster, and η is

"Harmonic analysis on real reductive groups. I. The theory of the constant term", Journal of Functional Analysis, 19: 104–204, doi:10.1016/0022-1236(75)90034-8

can be constructed using the Bernstein–Sato polynomial by taking the constant term of the Laurent expansion of f(x)s at s = −1. For arbitrary f(x) just

Because the constant of integration can be anything, the additional constant term can be absorbed into it. Finally, if theta is real-valued, we can indicate

while (a != 0 && b != 0) { if (b & 1) /* if the polynomial for b has a constant term, add the corresponding a to p */ p ^= a; /* addition in GF(2^m) is an

is T 3 A ( τ ) {\displaystyle T_{3A}(\tau )} where one can set the constant term a(0) = 42 (OEIS: A030197), j 3 A ( τ ) = T 3 A ( τ ) + 42 = ( ( η (

is of class Ti: that is, such that any system of polynomials with no constant term of degree dj in n variables has a non-trivial zero whenever n > Σ dji

If Q ( z ) {\displaystyle Q(z)} is a formal power series in z with constant term 1, we can define a multiplicative sequence K = 1 + K 1 + K 2 + ⋯ {\displaystyle

{\textstyle \phi (z)\in C[[z]]} be a formal power series with a non-zero constant term. Then the functional equation T ( z ) = z ϕ ( T ( z ) ) {\displaystyle

degree 2n − 1; (ii) the coefficients of Qn are all 1 or −1, and its constant term equals 1; and (iii) the identity |Pn(z)|2 + |Qn(z)|2 = 2(n + 1) holds

} up to ἴσ M {\displaystyle \mathrm {M} } the zeroth power (i.e. a constant term) ζ {\displaystyle \zeta } the unknown quantity (because a number x {\displaystyle

gravitation; the second is an additional force, analogous to the cosmological constant term in general relativity. However, the inverse-square potential is the

}{\frac {(-1)^{n}}{n!}}\gamma _{n}(a)(s-1)^{n}.} In particular, the constant term is given by lim s → 1 [ ζ ( s , a ) − 1 s − 1 ] = γ 0 ( a ) = − Γ ′

constructed above has the form S = I + L where L is polynomial in N without constant term. Any other square root T with positive eigenvalues has the form T =

2,048, 11,202, 49,152, ...} (OEIS: A097340) where one can set the constant term a(0) = 24, j 4 A ( τ ) = T 4 A ( τ ) + 24 = ( η 2 ( 2 τ ) η ( τ ) η

related to the characteristic polynomial of T {\displaystyle T} . The constant term in that polynomial (the term with ε = 0 {\displaystyle \varepsilon =0}

holomorphic functions of q. A level 1 quasimodular form is defined to be the constant term of an almost holomorphic modular form (considered as a polynomial in

, {\displaystyle \ \det g\ ,} both of which lead to a cosmological constant term rather than a bona fide interaction. Physically,   f μ ν   {\displaystyle

indeterminants over R, an element of S is quasiregular if and only its constant term is quasiregular as an element of R. Every element of the Jacobson radical

wrapping the string around a compact manifold. cosmological constant The constant term of the Lagrangian, inducing a term in the action proportional to the

distinction between "eigenvector" and "generalized eigenvector". where the constant term is multiplied by the identity matrix I. This ordering of the inner product

to apply one of the special cases listed below if possible. If the constant term a4 = 0, then one of the roots is x = 0, and the other roots can be found

from the solution of the homogeneous equation obtained by removing the constant term. hyperbolic function Hyperbolic functions are analogs of the ordinary

yanduan is the reverse of that in Ceyuan haijing, i.e., here with the constant term at top, followed by first order tian yuan, second order tian yuan, third

is T 4 A ( τ ) {\displaystyle T_{4A}(\tau )} where one can set the constant term a(0) = 24 (OEIS: A097340), j 4 A ( τ ) = T 4 A ( τ ) + 24 = ( η 2 (

is ρ = H 2 / 2 , {\displaystyle \rho =H^{2}/2,} which explains the constant term. The simplest way to apply the Euler–Lagrange equation to this problem

algebra, was used by Ivan Cherednik in his proof of the Macdonald's constant term conjecture. David Goldschmidt Group Characters, Symmetric Functions

R^{0}[[x]]\subset R[[x]]} the ideal consisting of power series without constant term. Then, given f ( x ) ∈ R 0 [ [ x ] ] {\displaystyle f(x)\in R^{0}[[x]]}

1988. It is notable because its character is the j-invariant with no constant term, j ( τ ) − 744 {\displaystyle j(\tau )-744} , and its automorphism group

with the model including cold dark matter (CDM) and the Λ cosmological constant term simulating the cosmic acceleration referred to as dark energy. The first

is a Kerr–de Sitter black hole. As in Hooke's law, the cosmological constant term depends linearly on distance from the origin, and the Kerr–de Sitter

industry. "n" is the number of firms in the industry, and "b" is a constant term representing the responsiveness of a firm's sales to its price. "Pfirm"

minors of B A {\displaystyle BA} while the right hand side will give the constant term of det ( z I m + A B ) {\displaystyle \det(zI_{m}+AB)} , which is simply

along geodesic cycles of Klein's J-function (normalized such that the constant term vanishes) is a harmonic Maass form of weight 1/2. The above abstract

is defined so that the Laurent expansion of ℘(z) at z = 0 has zero constant term. The fourth theta function – and thus the others too – is intimately

subring than R[A], and not necessarily commutative. In particular the constant term B0 = adj(−A) lies in R[A]. Since A is an arbitrary square matrix, this

original system a system can be found with non-singular Jacobian. The constant term in the Taylor series of the scaled bifurcation equation is called the

by a power of the indeterminate, getting a polynomial with a nonzero constant term. For k = 0 and k = n, Descartes' rule of signs shows that the polynomial

contain the rational numbers, so that the logarithm of power series with constant term 1 is defined (by log ⁡ ( 1 − t S ) = − ∑ i > 0 1 i ( t S ) i {\displaystyle

_{i\alpha }-\sigma _{j\alpha }\right)^{2}+\cdots } Ignoring the irrelevant constant term H0 = −JNd and passing to the continuum limit, given that we are interested

}(u{\overline {f}}).} Thus if f is a polynomial in z−1 without constant term H ε f → − i f {\displaystyle H_{\varepsilon }f\rightarrow -if} uniformly

1)\oplus f(1,0,0)\oplus f(1,0,1)} Since there are no variables with the constant term, a 0 = f 0 . {\displaystyle a_{0}=f_{0}.} For a term which includes

Green's function for the three-variable Laplace operator, apart from the constant term − 1 / ( 4 π ) {\displaystyle -1/(4\pi )} expressed in Cartesian coordinates

there is no affine function (a linear function with a possibly nonzero constant term) that assigns a non-negative value to each positive vector in the complementary

\dots ,\tau _{n})\prod _{j=1}^{n}x(t-\tau _{j})\,d\tau _{j}.} Here the constant term h 0 {\displaystyle h_{0}} on the right side is usually taken to be zero

the correct bank angle for the turn, but more seriously, changes the constant term in the characteristic equation to: ( W h − H Ω ) k A J {\displaystyle

two potentials v and v', differing by more than an additive spatially constant term, and their corresponding current densities j and j', the Heisenberg

participants one at a time) generates a new random polynomial with constant term zero and calculates for each remaining player a new ordered pair, where

a tangent vector amounts to a linear functional on I1 that has no constant term and kills the square of I1 and the formula (*) implies [ f , g ] = f

original PRF was of degree 2, so after reducing it by two degrees, only a constant term is left which, trivially, synthesises as a resistance. In step two of

is the area of g(D). The first determinant is by definition just the constant term in ef = |eg|2. Ahlfors 1966 Schiffer 1959, p. 261 Schiffer & Hawley

into current fluctuations and the measured photocurrent will include a constant term, I0, proportional to the mean optical intensity and a time dependent

A064984 C. Adiga, I. N. Cangul and H. N. Ramaswamy (2016). "On the constant term of the minimal polynomial of cos ⁡ ( 2 π n ) {\displaystyle \cos \left({\frac

SPn(C − {0}) with the space of monic polynomials of degree n having constant term different from zero, i.e. Cn − 1 × (C − {0}), which is homotopy-equivalent

}&&=17x^{2}+44x+29\end{aligned}}} The original triple comprises the constant term in each of the respective quadratic equations. Below is a sample output

{a}}_{c}+{\hat {\sigma }}_{-}{\hat {a}}_{c}^{\dagger }\right)} The constant term 1 2 ℏ ω c {\displaystyle {\frac {1}{2}}\hbar \omega _{c}} represents

\operatorname {ad} _{{\mathfrak {g}}'}(s)} is a polynomial without constant term in ad g ′ ⁡ ( x ) {\displaystyle \operatorname {ad} _{{\mathfrak {g}}'}(x)}

vector of a local flow on M; a first order differential operator without constant term in any local chart on M; a derivation of C∞(M). The last condition means

vector of a local flow on M; a first order differential operator without constant term in any local chart on M; a derivation of C∞(M). The last condition means

universal gravitation, the second one corresponds to the cosmological constant term in general relativity and McCrea-Milne cosmology. Then the field is

term is 1, all other coefficients are divisible by a prime, and the constant term is not divisible by the square of the prime. 3.  The Eisenstein criterion

}(u{\overline {f}}).}} Thus if f is a polynomial in z−1 without constant term H ε f → − i f {\displaystyle \displaystyle {H^{\varepsilon }f\rightarrow

cone of nullforms nullform A form on which all invariants with zero constant term vanish. octavic octic (Adjective) Degree 8 (Noun) A form of degree 8

polynomials in z are dense in A2(Ω) and polynomials in z−1 without constant term are dense in A2(Ωc), the image of U is dense in A2(Ω) ⊕ A2(Ωc). It can

infinity. In this case L = ∞ {\displaystyle L=\infty } and, thus, the constant term 4 in (5) disappears. The Freedman–He–Wang conjecture (1994) stated that

The remaining term is the negative of the particle's rest energy, a constant term which can be ignored in the Lagrangian. For the case of an interacting

Monstrous moonshine, can be written as a Fourier series in which the constant term is 744: j ( τ ) = q − 1 + 744 + 196 884 q + 21 493 760 q 2 + 864 299

transseries f {\displaystyle f} has a unique antiderivative with zero constant term F ∈ T L E {\displaystyle F\in \mathbb {T} ^{LE}} , F ′ = f {\displaystyle

constants, since these are just Fourier series of rapid decay without constant term. Warner 1983, pp. 220–221 Springer 1957, pp. 178–206 Springer 1957,

tangents passing through ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} . The constant term of a monic quadratic equation is always the product of its solutions