New formulas for the linearization coefficients of some nonsymmetric Jacobi polynomials

Advances in Difference Equations

Waleed M Abd-Elhameed¹ 

[1] Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

关键词: linearization coefficients;    hypergeometric functions;    Jacobi polynomials;    symbolic computation;    recurrence relations;    42C10;    33A50;    33C25;    33D45;   

DOI  :  10.1186/s13662-015-0509-4

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY