| Title:
|
A note on $q$-partial difference equations and some applications to generating functions and $q$-integrals (English) |
| Author:
|
Niu, Da-Wei |
| Author:
|
Cao, Jian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
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3 |
| Year:
|
2019 |
| Pages:
|
671-694 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$q$-partial difference equation |
| Keyword:
|
homogeneous generalized Al-Salam-Carlitz polynomial |
| Keyword:
|
generating function |
| Keyword:
|
Andrews-Askey integral |
| Keyword:
|
Ramanujan $q$-beta integral |
| MSC:
|
05A30 |
| MSC:
|
11B65 |
| MSC:
|
33D15 |
| MSC:
|
33D45 |
| MSC:
|
33D50 |
| MSC:
|
35C11 |
| idZBL:
|
Zbl 07088812 |
| idMR:
|
MR3989274 |
| DOI:
|
10.21136/CMJ.2018.0470-17 |
| . |
| Date available:
|
2019-07-24T11:17:00Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147785 |
| . |
| Reference:
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