On computing some special values of multivariate hypergeometric functions
type: Item
instance of: scholarly article
title: On computing some special values of multivariate hypergeometric functions
zbMATH Open document ID: 1312.33054
author: Giovanni Mingari Scarpello
author: Daniele Ritelli
published in: Journal of Mathematical Analysis and Applications
publication date: 2014-08-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1212.0251
review text: The authors establish interesting formulas for the values of the multivariate hypergeometric functions, including Appell and Lauricella \(F^{(n)}_D\) functions, at some special points inside and outside their disks of convergence. Relationships of hypergeometric functions' special values to certain complete elliptic integrals are also discussed. The basic tools are a well-established generalization of Kummer identity to multivariate hypergeometric functions, the usual representation for such functions and some reduction schemes of hyperelliptic integrals.
reviewed by: Allal Ghanmi
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 33C65
zbMATH DE Number: 6334382
zbMATH Keywords: Kummer identity
zbMATH Keywords: Eulerian integrals
zbMATH Keywords: multivariate hypergeometric function
zbMATH Keywords: Appell function
zbMATH Keywords: Lauricella function
zbMATH Keywords: complete elliptic integral of first kind
zbMATH Keywords: reduction of hyperelliptic integrals
MaRDI profile type: Publication
OpenAlex ID: W2171421692
Wikidata QID: Q58887684
arXiv ID: 1212.0251
cites work: Q4222737
cites work: Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations
cites work: Q3751634
cites work: Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind
cites work: Q5615009
cites work: Quadratic Transformations of Appell Functions
cites work: Elliptic Baker–Akhiezer functions and an application to an integrable dynamical system
cites work: On the geometry of elliptic solitons
cites work: Q5787146
cites work: Q5827353
cites work: Q5820721
cites work: Q3084090
cites work: Special values of the hypergeometric series
cites work: Special values of the hypergeometric series III
cites work: Lamé polynomials, hyperelliptic reductions and Lamé band structure
cites work: A transformation formula for Appell's hypergeometric function \(F_1\) and common limits of triple sequences by mean iterations
cites work: Some Transformation Formulas for Lauricella's Hypergeometric Functions FD
cites work: The hyperelliptic integrals and \(\pi \)
cites work: \(\pi\) and the hypergeometric functions of complex argument
cites work: Q3999257
cites work: On Epstein's Zeta-function.
cites work: Q4716292
cites work: Special values of the hypergeometric series. II
DOI: 10.1016/J.JMAA.2014.06.070
description: scientific article; zbMATH DE number 6334382