A Review of q-Difference Equations for Al-Salam–Carlitz Polynomials and Applications to U(n + 1) Type Generating Functions and Ramanujan’s Integrals-Reference-Cited by-同舟云学术

A Review of q-Difference Equations for Al-Salam–Carlitz Polynomials and Applications to U(n + 1) Type Generating Functions and Ramanujan’s Integrals

Published:2023-03-29 Issue:7 Volume:11 Page:1655
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Cao Jian¹^ORCID,Huang Jin-Yan¹,Fadel Mohammed²^ORCID,Arjika Sama³^ORCID

Affiliation:

1. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

2. Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

3. Department of Mathematics and Informatics, University of Agadez, Agadez 900288, Niger

Abstract

In this review paper, our aim is to study the current research progress of q-difference equations for generalized Al-Salam–Carlitz polynomials related to theta functions and to give an extension of q-difference equations for q-exponential operators and q-difference equations for Rogers–Szegö polynomials. Then, we continue to generalize certain generating functions for Al-Salam–Carlitz polynomials via q-difference equations. We provide a proof of Rogers formula for general Al-Salam–Carlitz polynomials and obtain transformational identities using q-difference equations. In addition, we gain U(n+1)-type generating functions and Ramanujan’s integrals involving general Al-Salam–Carlitz polynomials via q-difference equations. Finally, we derive two extensions of the Andrews–Askey integral via q-difference equations.

Funder

Zhejiang Provincial Natural Science Foundation

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/7/1655/pdf

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