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

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.