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Find link is a tool written by Edward Betts.Longer titles found: Hypergeometric function of a matrix argument (view), Confluent hypergeometric function (view), Generalized hypergeometric function (view), General hypergeometric function (view)
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Wilf–Zeilberger pair
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In mathematics, specifically combinatorics, a Wilf–Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identitiesKazuhiko Aomoto (70 words) [view diff] exact match in snippet view article find links to article
is a Japanese mathematician who introduced the Aomoto-Gel'fand hypergeometric function and the Aomoto integral. He was a professor at Nagoya UniversityHahn–Exton q-Bessel function (832 words) [view diff] exact match in snippet view article find links to article
_{1}(0;q^{\nu +1};q,qx^{2}).} ϕ{\displaystyle \phi } is the basic hypergeometric function. Koelink and Swarttouw proved that Jν(3)(x;q){\displaystyle J_{\nuList of factorial and binomial topics (218 words) [view diff] exact match in snippet view article find links to article
coefficient Gould's sequence Hyperfactorial Hypergeometric distribution Hypergeometric function identities Hypergeometric series Incomplete beta function IncompleteList of mathematical identities (168 words) [view diff] exact match in snippet view article find links to article
Combinatorial Fibonacci identities and Other Fibonacci identities Hypergeometric function identities List of integrals of logarithmic functions List of topicsAppell sequence (1,302 words) [view diff] exact match in snippet view article find links to article
Appell polynomials can be obtained in terms of the generalized hypergeometric function. Let Δ(k,−n){\displaystyle \Delta (k,-n)} denote the array of k{\displaystyleQ-Charlier polynomials (249 words) [view diff] exact match in snippet view article find links to article
their properties. The polynomials are given in terms of the basic hypergeometric function by Cn(q−x;a;q)=2ϕ1(q−n,q−x;0;q,−qn+1/a).{\displaystyle \displaystyleBessel–Clifford function (1,125 words) [view diff] exact match in snippet view article find links to article
Bessel–Clifford function is up to a scaling factor a Pochhammer–Barnes hypergeometric function; we have Cn(z)=π(n) 0F1(;n+1;z).{\displaystyle {\mathcal {C}}_{n}(z)=\piBeta wavelet (1,684 words) [view diff] exact match in snippet view article find links to article
The beta wavelet spectrum can be derived in terms of the Kummer hypergeometric function. Let ψbeta(t|α,β)↔ΨBETA(ω|α,β){\displaystyle \psi _{beta}(t|\alphaIndex of combinatorics articles (626 words) [view diff] exact match in snippet view article find links to article
Perfect hash function Heilbronn triangle problem Helly family Hypergeometric function identities Hypergeometric series Hypergraph Incidence structureSpiral (4,239 words) [view diff] exact match in snippet view article find links to article
superspirals with completely monotonic curvature given in terms of Gauss hypergeometric function. Computer Aided Geometric Design 29(7): 510–518, 2012 [9]. ZiatdinovEuler spiral (2,754 words) [view diff] exact match in snippet view article find links to article
superspirals with completely monotonic curvature given in terms of Gauss hypergeometric function", Computer Aided Geometric Design, 29 (7): 510–518 Constantin (2016-03-07)Generalized integer gamma distribution (1,548 words) [view diff] exact match in snippet view article find links to article
1F1(a,b;z){\displaystyle _{1}F_{1}(a,b;z)} is the Kummer confluent hypergeometric function. This function has usually very good convergence properties andFisher transformation (1,480 words) [view diff] exact match in snippet view article find links to article
{1+r\rho }{2}}\right)} where F{\displaystyle F} is the Gaussian hypergeometric function and ν=N−1>1{\displaystyle \nu =N-1>1} . While the Fisher transformationLerch zeta function (3,186 words) [view diff] exact match in snippet view article find links to article
{\displaystyle |a|<1;\Re (s)<0.} The representation as a generalized hypergeometric function is Φ(z,s,α)=1αss+1Fs(1,α,α,α,⋯1+α,1+α,1+α,⋯∣z).{\displaystyle \PhiJackson q-Bessel function (2,424 words) [view diff] exact match in snippet view article find links to article
functions are given in terms of the q-Pochhammer symbol and the basic hypergeometric function ϕ{\displaystyle \phi } by Jν(1)(x;q)=(qν+1;q)∞(q;q)∞(x/2)ν2ϕ1(0Confidence distribution (3,934 words) [view diff] exact match in snippet view article find links to article
{1}{2}};{\frac {1+r\rho }{2}})} where F{\displaystyle F} is the Gaussian hypergeometric function and ν=n−1>1{\displaystyle \nu =n-1>1} . This is also the posteriorLambert W function (10,544 words) [view diff] exact match in snippet view article find links to article
that function. In this respect, the generalization resembles the hypergeometric function and the Meijer G function but it belongs to a different class ofDistribution of the product of two random variables (6,945 words) [view diff] exact match in snippet view article find links to article
\;\;\;0<z<1} where 2F1{\displaystyle {_{2}F_{1}}} is the Gauss hypergeometric function defined by the Euler integral 2F1(a,b,c,z)=Γ(c)Γ(a)Γ(c−a)∫01vaModified half-normal distribution (1,673 words) [view diff] case mismatch in snippet view article find links to article
Maitland (1935). "The Asymptotic Expansion of the Generalized Hypergeometric Function". Journal of the London Mathematical Society. s1-10 (4): 286–293Gradshteyn and Ryzhik (11,910 words) [view diff] exact match in snippet view article find links to article
"The integrals in Gradshteyn and Ryzhik. Part 28: The confluent hypergeometric function and Whittaker functions" (PDF). Scientia. Series A: Mathematical