Combinatorial Proofs of Ismail's Identities on Al-Salam--Chirara Polynomials

TL;DR

This paper introduces combinatorial proofs for two identities related to Al-Salam--Chirara polynomials, providing new insights through partition theoretic generating functions.

Contribution

It offers novel combinatorial proofs of Ismail's identities, expanding the understanding of these polynomial identities with partition theory methods.

Findings

New combinatorial proofs of Ismail's identities

Partition theoretic generating function interpretations

Enhanced understanding of Al-Salam--Chirara polynomials

Abstract

We present new proofs of two identities arising in the work of Mourad Ismail using partition theoretic generating function interpretations.