Certain results on Wright's generalized hypergeometric functions with applications
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.33007
author: Jeta Ram
author: R. K. Saxena
publication date: 2001-04-24T00:00:00Z
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 1590502
zbMATH Keywords: beta integral
zbMATH Keywords: digamma function
MaRDI profile type: Publication
title: Certain results on Wright's generalized hypergeometric functions with applications
published in: The Journal of the Indian Academy of Mathematics
review text: The authors study the integral \(I=\int^1_{-1}(1-x)^a(1+x)^b f({1 \over 2}(1-x))dx\), where \(f\) is a gamma fraction multiplied by a Wright hypergeometric function \(_{p+2}\psi_{q+2}\) with certain conditions on some of the parameters. Using term-by-term integration, they establish an expression of \(I\) in terms of \(_{q+4}\Psi_{q+3}\). Moreover, the partial derivatives \(\partial I/ \partial a\) and \(\partial I/ \partial b\) are found; these expressions include series involving the digamma function. A number of special cases are considered as well as some formulas obtained by comparison with known summation theorems.
reviewed by: Per W. Karlsson
description: scientific article