文章基本信息

标题：Linearization coefficients of some particular Jacobi polynomials via hypergeometric functions
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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：2016
卷号：2016
期号：1
页码：91
DOI：10.1186/s13662-016-0826-2
语种：English
出版社：Hindawi Publishing Corporation
摘要：The main purpose of the present paper is to establish two new linearization formulas for certain Jacobi polynomials. The new established formulas are expressed in terms of terminating hypergeometric functions of the type F 3 4 ( 1 ) ${}_{4}F_"(1)$ . In virtue of the well-known Pfaff-Saalschütz identity, or by using some computer algebra algorithms, and in particular, the algorithms of Zeilberger, Petkovsek and van Hoeij, the resulting F 3 4 ( 1 ) ${}_{4}F_"(1)$ can be reduced for particular choices of the involved parameters. This reduction leads to obtaining several simple linearization formulas of some particular Jacobi polynomials free of any hypergeometric functions.
关键词：Jacobi polynomials ; linearization coefficients ; generalized hypergeometric functions ; computer algebra algorithms