文章基本信息

标题：New formulas for the linearization coefficients of some nonsymmetric Jacobi polynomials
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作者：Waleed M Abd-Elhameed
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：168
DOI：10.1186/s13662-015-0509-4
语种：English
出版社：Hindawi Publishing Corporation
摘要：The main aim of this paper is to develop four innovative linearization formulas for some nonsymmetric Jacobi polynomials. This means that we find the coefficients of the products of Jacobi polynomials of certain parameters. In general, these coefficients are expressed in terms of certain hypergeometric functions of the unit argument. We employ some symbolic algebraic computations such as the algorithms of Zeilberger, Petkovsek and van Hoeij for reducing such coefficients. Moreover, and based on a certain Whipple transformation, two new closed formulas for summing certain terminating hypergeometric functions of the unit argument are deduced. New formulas for some definite integrals are given with the aid of the derived linearization formulas.
关键词：linearization coefficients ; hypergeometric functions ; Jacobi polynomials ; symbolic computation ; recurrence relations