Probabilistic derivation of some generating functions for the Laguerre polynomials

被引：2

作者：

Lee, PA ^{[1
]}

Ong, SH

Srivastava, HM

机构：

[1] Univ Telekom Jalan Ayer Keroh Lama, Fac Informat Technol, Melaka 75450, Malaysia

[2] Univ Malaya, Dept Math, Kuala Lumpur 50603, Malaysia

[3] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 1999年 / 38卷 / 7-8期

基金：

加拿大自然科学与工程研究理事会;

关键词：

generating functions; Laguerre polynomials; hypergeometric function; noncentral negative binomial distribution; Poisson distribution; group-theoretic method; probability mass function; probability generating function; bilinear generating functions;

D O I：

10.1016/S0898-1221(99)00234-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A well-known generating function of the classical Laguerre polynomials was recently rederived probabilistically by Lee. In this paper, some other (presumably new) generating functions for the Laguerre polynomials are derived by means of probabilistic considerations. A direct (analytical) proof of each of these generating functions is also presented for the sake of completeness. (C) 1999 Elsevier Science Ltd. All rights reserved.

引用

页码：21 / 29

页数：9

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