On a generalized homogeneous Hahn polynomial

作     者：Bing He 

作者机构：School of Mathematics and StatisticsCentral South UniversityChangsha 410083China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第5期

页      面：957-976页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11801451) the Natural Science Foundation of Hunan Province(Grant No.2020JJ5682). 

主　　题：generalized homogeneous Hahn polynomial generating function asymptotic expansion zeros zeros of entire functions q-congruence 

摘      要：We investigate a generalized homogeneous Hahn polynomial in some detail. This polynomial includes as special cases the homogeneous Hahn polynomial and the homogeneous Rogers-Szeg o polynomial.A generating function, which contains a known generating function as a special case, is given. We also give a finite series generating function. Some results on the asymptotic expansion for this polynomial are derived.Certain results on zeros are also obtained. We deduce several results on zeros of certain entire functions involving this generalized Hahn polynomial. As results, one of Zhang(2017)’s results as well as others is obtained. Finally,we derive several general results on q-congruences of the generalized q-Apéry polynomials, from which two qcongruences involving the generalized homogeneous Hahn polynomial are deduced.