On a generalized homogeneous Hahn polynomial  

作　　者：Bing He 

机构地区：[1]School of Mathematics and Statistics,Central South University,Changsha 410083,China

出　　处：《Science China Mathematics》2023年第5期957-976,共20页中国科学：数学（英文版）

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

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.

关 键 词：generalized homogeneous Hahn polynomial generating function asymptotic expansion ZEROS zeros of entire functions q-congruence 

分 类 号：O174.14[理学—数学]