Orthogonality relations and generating functions for Jacobi polynomials and related hypergeometric functions
type: Item
instance of: scholarly article
title: Orthogonality relations and generating functions for Jacobi polynomials and related hypergeometric functions
zbMATH Open document ID: 0847.33005
DOI: 10.1016/0096-3003(94)00092-I
author: Ming-Po Chen
author: H. M. Srivastava
published in: Applied Mathematics and Computation
publication date: 1995-05-11T00:00:00Z
full work available at URL: https://eudml.org/doc/43987
review text: The authors begin by examining the validity of some orthogonality relations and expansion formulas [asserted recently by \textit{S. D. Bajpai}, Panam. Math. J. 3, No. 1, 95-102 (1993; Zbl 0845.33004)] involving a class of hypergeometric polynomials which are essentially certain modified Jacobi polynomials. The corrected version of each of these orthogonality relations is shown to follow readily from the familiar orthogonality property of the classical Jacobi polynomials. A brief discussion is then presented about the applicability of an orthogonality property for the first few Jacobi polynomials, but over a semi-infinite interval, which was considered by \textit{V. Romanovski} [C. R. Acad. Sci., Paris 188, 1023-1025 (1929)] and (more recently) by \textit{S. D. Bajpai} [Nat. Acad. Sci. Lett. 15, 221-226 (1992)]. Several families of generating functions for Jacobi and Laguerre polynomials, and for various related hypergeometric functions in one and more variables, are also considered systematically.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 753902
zbMATH Keywords: Jacobi polynomials
MaRDI profile type: Publication
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OpenAlex ID: W1985878120
description: scientific article; zbMATH DE number 753902