A Note on q-Partial Difference Equations and Some Applications to Generating Functions and q-Integrals

被引：3

作者：

Niu, Da-Wei ^{[1
]}

Cao, Jian ^{[2
]}

机构：

[1] East China Normal Univ, Sch Math Sci, 500 Dongchuan Rd, Shanghai 200241, Peoples R China

[2] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2019年 / 69卷 / 03期

关键词：

q-partial difference equation; homogeneous generalized Al-Salam-Carlitz polynomial; generating function; Andrews-Askey integral; Ramanujan q-beta integral; Q-EXTENSION; SUMMATION; BETA;

D O I：

10.21136/CMJ.2018.0470-17

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the condition on expanding an analytic several variables function in terms of products of the homogeneous generalized Al-Salam-Carlitz polynomials. As applications, we deduce bilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. We also gain multilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. Moreover, we obtain generalizations of Andrews-Askey integrals and Ramanujan q-beta integrals. At last, we derive U(n + 1) type generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials.

引用

页码：671 / 694

页数：24

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