A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials
Combinatorics
2020-12-01 v1 Classical Analysis and ODEs
Functional Analysis
Number Theory
Abstract
In this paper, we deduce the generalized -difference equations for general Al-Salam--Carlitz polynomials and generalize Arjika's recently results [-difference equation for homogeneous -difference operators and their applications, J. Differ. Equ. Appl. {\bf 26}, 987--999 (2020)]. In addition, we obtain transformational identities by the method of -difference equation. Moreover, we deduce type generating functions and Ramanujan's integrals involving general Al-Salam--Carlitz polynomials by -difference equation.
Cite
@article{arxiv.2011.05848,
title = {A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials},
author = {Jian Cao and Binbin Xu and Sama Arjika},
journal= {arXiv preprint arXiv:2011.05848},
year = {2020}
}
Comments
14 pages