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

Advances in Difference Equations

article

Cao, Jian¹  Xu, Binbin¹  Arjika, Sama² 

[1] Department of Mathematics, Hangzhou Normal University;Department of Mathematics and Informatics, University of Agadez

关键词: q -Difference equation;    q -Difference operator;    Al-Salam–Carlitz polynomials;    Generating functions;    Ramanujan’s integral;   

DOI  :  10.1186/s13662-020-03133-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we deduce the generalized q-difference equations for general Al-Salam–Carlitz polynomials and generalize Arjika’s recent results (Arjika in J. Differ. Equ. Appl. 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.

【 授权许可】

CC BY