Title

New Proofs Of Some Q-Series Results

Keywords

Askey-wilson operators; Delta operators; Polynomial bases; Sheffer classification; The q-exponential function ε

Abstract

We use a Sheffer classification technique to give very short proofs of the addition theorem for the εq function, the representation of εq as a multiple of a 2φ1, and a relatively new representation of εq. A direct proof of the evaluation of the connection coefficients of the Askey-Wilson polynomials and the Nassrallah-Rahman integral are also given. A simple proof of a characterization theorem for the continuous q-Hermite polynomials is also given. © 2005 Springer Science+Business Media, Inc.

Publication Date

1-1-2005

Publication Title

Developments in Mathematics

Volume

13

Number of Pages

287-299

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/0-387-24233-3_12

Socpus ID

84859488450 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84859488450

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