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

Abstract

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

Keywords:

• Basic (q-) hypergeometric series
• q-difference equation
• homogeneous q-difference operator
• Cauchy polynomials
• Hahn polynomials
• generating functions

2010 Mathematics Subject Classifications:

• Primary 05A30
• 33D15
• 33D45
• Secondary05A40
• 11B65

Acknowledgments

The author would like to thank the referees and editors for their many valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).