Contiguous relations of hypergeometric series

DOI10.1016/S0377-0427(02)00643-XzbMath1018.33001arXivmath/0109222OpenAlexW2120094609MaRDI QIDQ1874187

Raimundas Vidunas

Publication date: 22 May 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0109222

zbMATH Keywords

Gauss hypergeometric functioncontiguous relation

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (24)

A reduction formula for a \(q\)-beta integral ⋮ A hypergeometric integral with applications to the fundamental solution of Laplace's equation on hyperspheres ⋮ Contiguous relations and their computations for \(_2F_1\) hypergeometric series ⋮ Periods of Hodge cycles and special values of the Gauss' hypergeometric function ⋮ Hypergeometric series with gamma product formula ⋮ Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and \(q\)-Kummer identities ⋮ Some formulas for Horn's hypergeometric function \(\mathrm{G}_B\) of three variables ⋮ Symmetries of coefficients of three-term relations for the hypergeometric series ⋮ Bernstein-type bounds for beta distribution ⋮ Contiguous relations for \(_{2}F_{1}\) hypergeometric series ⋮ On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters ⋮ Zeros of Orthogonal Polynomials ⋮ Three-term relations for \(_3F_2(1)\) ⋮ Three-term relations for basic hypergeometric series ⋮ On some new contiguous relations for the Gauss hypergeometric function with applications ⋮ On the contiguous relations of hypergeometric series ⋮ Contiguous function relations for \(k\)-hypergeometric functions ⋮ Hypexp 2, expanding hypergeometric functions about half-integer parameters ⋮ Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions ⋮ Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters ⋮ Interlacing of the zeros of Jacobi polynomials with different parameters ⋮ Interlacing of the zeros of contiguous hypergeometric functions ⋮ Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications ⋮ Contiguous Relations and Creative Telescoping

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