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

Autor:	Niu, Da-Wei
Další autoři:	Cao, Jian
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles Ramanujan $q$-beta integral Andrews-Askey integral $q$-partial difference equation homogeneous generalized Al-Salam-Carlitz polynomial generating function
Druh dokumentu:	Non-fiction
ISSN:	0011-4642
Abstrakt:	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.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Plný text Full text from SpringerLink