A note on q -partial difference equations and some applications to generating functions and q -integrals

Da-Wei Niu; Jian Cao

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 3, page 671-694
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Niu, Da-Wei, and Cao, Jian. "A note on $q$-partial difference equations and some applications to generating functions and $q$-integrals." Czechoslovak Mathematical Journal 69.3 (2019): 671-694. <http://eudml.org/doc/294669>.

@article{Niu2019,
abstract = {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.},
author = {Niu, Da-Wei, Cao, Jian},
journal = {Czechoslovak Mathematical Journal},
keywords = {$q$-partial difference equation; homogeneous generalized Al-Salam-Carlitz polynomial; generating function; Andrews-Askey integral; Ramanujan $q$-beta integral},
language = {eng},
number = {3},
pages = {671-694},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on $q$-partial difference equations and some applications to generating functions and $q$-integrals},
url = {http://eudml.org/doc/294669},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Niu, Da-Wei
AU - Cao, Jian
TI - A note on $q$-partial difference equations and some applications to generating functions and $q$-integrals
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 671
EP - 694
AB - 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.
LA - eng
KW - $q$-partial difference equation; homogeneous generalized Al-Salam-Carlitz polynomial; generating function; Andrews-Askey integral; Ramanujan $q$-beta integral
UR - http://eudml.org/doc/294669
ER -

References

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