Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:407

Article

Cohl, Howard S.¹  MacKenzie, Connor^1,2  Volkmer, Hans³ 

[1] NIST, Appl & Computat Math Div, Gaithersburg, MD 20899 USA

[2] Westminster Coll, Dept Math, New Wilmington, PA 16172 USA

[3] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

关键词: Orthogonal polynomials;    Generating functions;    Connection coefficients;    Generalized hypergeometric functions;    Eigenfunction expansions;    Definite integrals;   

DOI  :  10.1016/j.jmaa.2013.04.067

来源: Elsevier

【 摘 要 】

We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using connection relations with one free parameter for these orthogonal polynomials. We also use orthogonality relations to determine corresponding definite integrals. Published by Elsevier Inc.

【 授权许可】

Free