English

Two $q$-operational equations and Hahn polynomials

Classical Analysis and ODEs 2022-11-08 v2

Abstract

Motivated by Liu's recent work in \cite{Liu2022}. We shall reveal the essential feature of Hahn polynomials by presenting two new qq-exponential operators. These lead us to use a systematic method to study identities involving Hahn polynomials. As applications, we use the method of qq-exponential operator to prove the bilinear generating function of Hahn polynomials and Heine's second transformation formula. Moreover, a generalization of qq-Gaussian summation is given, too.

Keywords

Cite

@article{arxiv.2210.15618,
  title  = {Two $q$-operational equations and Hahn polynomials},
  author = {Jing Gu and DunKun Yang and Qi Bao},
  journal= {arXiv preprint arXiv:2210.15618},
  year   = {2022}
}
R2 v1 2026-06-28T04:39:47.562Z