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A moment sequence in the q-world

Anna Kula (2007)

Banach Center Publications

The aim of the paper is to present some initial results about a possible generalization of moment sequences to a so-called q-calculus. A characterization of such a q-analogue in terms of appropriate positivity conditions is also investigated. Using the result due to Maserick and Szafraniec, we adapt a classical description of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity to the q-situation. This makes a link between q-positive definiteness and q-complete...

A new proof of the q -Dixon identity

Victor J. W. Guo (2018)

Czechoslovak Mathematical Journal

We give a new and elementary proof of Jackson’s terminating q -analogue of Dixon’s identity by using recurrences and induction.

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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