Classical orthogonal polynomials as moments

被引：36
|
作者：
Ismail, MEH [1 ]
Stanton, D [1 ]
机构：
[1] UNIV MINNESOTA,SCH MATH,MINNEAPOLIS,MN 55455
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 1997年 / 49卷 / 03期
关键词：
classical orthogonal polynomials; Al-Salam-Chihara polynomials; continuous q-ultraspherical polynomials; generating functions; multilinear generating functions; transformation formulas; umbral calculus;
D O I：
10.4153/CJM-1997-024-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures. We use this fact to derive bilinear rind multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials.
引用
收藏
页码：520 / 542
页数：23
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