$q$-difference equations for homogeneous $q$-difference operators and their applications

TL;DR

This paper demonstrates how to derive generating functions from existing work using $q$-difference equations and explores the connections between transformation formulas and homogeneous $q$-difference equations.

Contribution

It introduces a method to obtain generating functions from prior results via $q$-difference equations and links transformation formulas with these equations.

Findings

Derived various generating functions using $q$-difference equations.

Established relations between transformation formulas and homogeneous $q$-difference equations.

Provided a framework connecting $q$-difference equations with generating functions.

Abstract

In this short paper, we show how to deduce several types of generating functions from Srivastava {\it et al} [Appl. Set-Valued Anal. Optim. {\bf 1} (2019), pp. 187-201.] by the method of $q$-difference equations. Moreover, we build relations between transformation formulas and homogeneous $q$-difference equations.