Integral And Series Representations Of Q -Polynomials And Functions: Part I

Keywords

basic hypergeometric series; bilateral hypergeometric series; connection relations; Fourier transforms; Mellin transforms; multiplication formulas; q - 1 -Hermite polynomials; q -Bessel functions; q -exponential functions; q -Laguerre polynomials; Ramanujan function; Stieltjes-Wigert polynomials

Abstract

By applying an integral representation for qk2, we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of q-functions and polynomials that naturally arise from combinatorics, analysis, and orthogonal polynomials corresponding to indeterminate moment problems. These functions include q-Bessel functions, the Ramanujan function, Stieltjes-Wigert polynomials, q-Hermite and q-1-Hermite polynomials, and the q-exponential functions eq, Eq and q. Their representations are in turn used to derive many new identities involving q-functions and polynomials. In this paper, we also present contour integral representations for the above mentioned functions and polynomials.

Publication Date

3-1-2018

Publication Title

Analysis and Applications

Volume

16

Issue

2

Number of Pages

209-281

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1142/S0219530517500129

Socpus ID

85041692967 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85041692967

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