Bilinear generating functions of the multivariable Al-Salam-Carlitz polynomials and applications

Qi Chen; Xinrong Ma; Jin Wang

Bilinear generating functions of the multivariable Al-Salam-Carlitz polynomials and applications

Combinatorics 2026-07-25 v1

Authors: Qi Chen , Xinrong Ma , Jin Wang

Abstract

In this paper, by the method of comparing coefficients, we establish a new generating function of multivariable Al-Salam-Carlitz polynomials which contains both Rogers' and Bowman's symmetirc expansion formulas and the classical $q$ -Mehler formula as special cases. Some new $q$ -series identities related to the multivariable Al-Salam-Carlitz polynomials are also presented.

Keywords

Al-Salam-Carlitz polynomials multivariable generating functions q-series identities Rogers expansion Bowman expansion

Cite

@article{arxiv.2607.23104,
  title  = {Bilinear generating functions of the multivariable Al-Salam-Carlitz polynomials and applications},
  author = {Qi Chen and Xinrong Ma and Jin Wang},
  journal= {arXiv preprint arXiv:2607.23104},
  year   = {2026}
}

Comments

19 pages