Linearization formulae for certain Jacobi polynomials
Date
2016
Journal Title
Journal ISSN
Volume Title
Type
Article
Publisher
SPRINGER
Series Info
RAMANUJAN JOURNAL;Volume: 39 Issue: 1 Pages: 155-168
Scientific Journal Rankings
Abstract
In this article, some new linearization formulae of products of Jacobi polynomials for certain parameters are derived. These new derived formulae are expressed in terms of hypergeometric functions of unit argument, and they generalize some existing formulae in the literature. With the aid of some standard formulae and also by employing symbolic algebraic computation, and in particular Zeilberger's algorithm, several reduction formulae for summing certain terminating hypergeometric functions of unit argument are given, and hence several linearization formulae of products of Jacobi polynomials for special parameters free of hypergeometric functions are deduced.
Description
Accession Number: WOS:000367685700011
Keywords
University of Jacobi polynomials; Linearization problems; Generalized hypergeometric functions; Algorithms by Zeilberger, Petkovsek and van Hoeij, CONNECTION COEFFICIENTS; RECURRENCE RELATIONS; SERIES; PRODUCT; EXPANSIONS
Citation
Cited References in Web of Science Core Collection: 30