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arXiv · 2011.05848

A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials

Jian Cao·Binbin Xu·Sama Arjika
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Abstract

In this paper, we deduce the generalized $q$-difference equations for general Al-Salam--Carlitz polynomials and generalize Arjika's recently results [$q$-difference equation for homogeneous $q$-difference operators and their applications, J. Differ. Equ. Appl. {\bf 26}, 987--999 (2020)]. In addition, we obtain transformational identities by the method of $q$-difference equation. Moreover, we deduce $U(n+1)$ type generating functions and Ramanujan's integrals involving general Al-Salam--Carlitz polynomials by $q$-difference equation.

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Jian Cao, Binbin Xu, Sama Arjika. 2020-11-10. A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials. https://doi.org/10.1186/s13662-020-03133-7

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