Explicit Forms of q-Deformed Lévy-Meixner Polynomials and Their Generating Functions  

作　　者：Zhi Yuan HUANG Pei Yan LI Ying WU 

机构地区：[1]Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第2期201-214,共14页数学学报（英文版）

基　　金：Project Nos.10571065 and 10401011 supported by NSFC

摘　　要：The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case （q=1） and fermionic case （q=-1）.In particular, when q=0 it＇s also compatible with the free case.The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case （q=1） and fermionic case （q=-1）.In particular, when q=0 it＇s also compatible with the free case.

关 键 词：Q-DEFORMATION Levy-Meixner polynomials generating function free probability 

分 类 号：O151[理学—数学]