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 -exponential operators. These lead us to use a systematic method to study identities involving Hahn polynomials. As applications, we use the method of -exponential operator to prove the bilinear generating function of Hahn polynomials and Heine's second transformation formula. Moreover, a generalization of -Gaussian summation is given, too.
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}
}