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

Da-Wei Niu, Jian Cao (2019)

Czechoslovak Mathematical Journal

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 ) ...

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