Recursion formulas for Appell's hypergeometric function \(F_2\) with some applications to radiation field problems
type: Item
instance of: scholarly article
title: Recursion formulas for Appell's hypergeometric function \(F_2\) with some applications to radiation field problems
zbMATH Open document ID: 1163.33006
author: Sheldon Opps
author: Nasser Saad
author: H. M. Srivastava
published in: Applied Mathematics and Computation
publication date: 2009-02-25T00:00:00Z
review text: A number of interesting new recursion formulae for the Appell functions \(F_2(\sigma,\alpha_1\alpha_2\pm n;\beta_1, \beta_2; x,y)\) and \(F_2(\sigma,\alpha_1 \alpha_2; \beta_1, \beta_2\pm n; x,y)\), where \(n\in N_0= \{0,11,2,\dots\}\), are derived by using some contiguous function relations for the Gauss hypergeometric series \(_2F_1\). The authors discuss applications of their results to the evaluation of radiation field integrals. A number of new reduction formulae is also established. Using these formulas, a number of numerical identities of multiple hypergeometric functions is also derived.
reviewed by: C. L. Parihar
Mathematics Subject Classification ID: 33C65
Mathematics Subject Classification ID: 33C90
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 5518812
zbMATH Keywords: multiple hypergeometric functions
zbMATH Keywords: Appell functions
zbMATH Keywords: recursion formulas
zbMATH Keywords: integral representations
zbMATH Keywords: Gauss hypergeometric function
zbMATH Keywords: generalized hypergeometric series
zbMATH Keywords: reduction and transformation formulas
zbMATH Keywords: contiguous function relations
zbMATH Keywords: radiation field integrals
zbMATH Keywords: applications and numerical results
MaRDI profile type: Publication
full work available at URL: j.amc.2008.11.006
OpenAlex ID: W1973207665
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DOI: 10.1016/J.AMC.2008.11.006
description: scientific article; zbMATH DE number 5518812