Some families of hypergeometric polynomials and associated integral representations
type: Item
instance of: scholarly article
title: Some families of hypergeometric polynomials and associated integral representations
zbMATH Open document ID: 1048.33012
author: Shy-Der Lin
author: Yi-Shan Chao
author: H. M. Srivastava
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-10T00:00:00Z
review text: In this paper the authors consider four families of polynomials, which are special or limiting cases of polynomials of the form \[ S_{n}^{N}(z):=\sum_{k=0}^{[n/N]}\frac{(-n)_{Nk}}{k!}\,A_{n,\,k}\,z^{k}, \] where \(A_{n,\,m}\) is a suitably bounded double sequence of real or complex numbers. They derive some single-, double-, and triple-integral representations associated with these families of polynomials. They also consider several known or new special cases and consequences of their main results, involving classical orthogonal polynomials and various other related hypergeometric polynomials. Concluding their investigation, the authors remark that each of the integral representation obtained in this paper, may be viewed as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 33C99
zbMATH DE Number: 2085963
zbMATH Keywords: hypergeometric polynomials
zbMATH Keywords: integral representations
zbMATH Keywords: linearization relationship
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.024
OpenAlex ID: W2117173602
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DOI: 10.1016/J.JMAA.2004.01.024
description: scientific article; zbMATH DE number 2085963