q-integral and moment representations for q-orthogonal polynomials

被引：18

作者：

Ismail, MEH ^{[1
]}

Stanton, D

机构：

[1] Univ S Florida, Dept Math, Tampa, FL 33620 USA

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2002年 / 54卷 / 04期

关键词：

q-integral; q-orthogonal polynomials; associated polynomials; q-difference equations; generating functions; Al-Salam-Chihara polynomials; continuous q-ultraspherical polynomials;

D O I：

10.4153/CJM-2002-027-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas far combinations of basic hypergeometric functions, including a new representation of the q-exponential function epsilon(q).

引用

页码：709 / 735

页数：27

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