English

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

Keywords

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

R2 v1 2026-06-23T20:05:15.313Z