Some expansion formulae for Fox's \(H\)-function of two variables involving associated Legendre functions
type: Item
instance of: scholarly article
title: Some expansion formulae for Fox's \(H\)-function of two variables involving associated Legendre functions
zbMATH Open document ID: 0791.33010
DOI: 10.1007/BF01904035
published in: Analysis Mathematica
publication date: 1994-03-27T00:00:00Z
review text: Using the orthogonality property of associated Legendre functions and the integral formula: \[ \int^{+1}_{-1}(1-x)^{{-m\over 2}}(1+x)^ kP_ m^ k(x)dx={(-1)^{{m\over 2}}2^{k-m+1}\Gamma(k+1)\Gamma(k- m+1)\over\Gamma(k+n-m+2)\Gamma(k-n-m+1)},R(k)>m -1, \] the author first evaluates four integrals involving Fox's \(H\)-function of two variables. He then uses these results in establishing eight expansion formulas of the \(H\)-function of two variables in terms of the \(H\)-function and products of associated Legendre functions.
Mathematics Subject Classification ID: 33C60
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 500207
zbMATH Keywords: Legendre functions
author: S. D. Bajpai
reviewed by: C. M. Joshi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 500207