Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Baeder, Michael A.¹  Cohl, Howard S.²  Volkmer, Hans³ 

[1] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

[2] NIST, Appl & Computat Math Div, Gaithersburg, MD 20899 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.2015.01.074

来源: Elsevier

【 摘 要 】

We use connection relations and series rearrangement to generalize generating functions for several higher continuous orthogonal polynomials in the Askey scheme, namely the Wilson, continuous dual Hahn, continuous Hahn, and Meixner-Pollaczek polynomials. We also determine corresponding definite integrals using the orthogonality relations for these polynomials. Published by Elsevier Inc.

【 授权许可】

Free