q-Difference Equation for the Operator E ̃(x,a;θ) and their Applications for the Polynomials h_n (a,b,x|q^(-1))

Mahmood A. Arif; Husam L. Saad

doi:10.24996/ijs.2023.64.6.28

Authors

Mahmood A. Arif Department of Mathematics, College of Education for Pure Sciences,University of Basrah, Basrah, Iraq
Husam L. Saad Department of Mathematics, College of Science,University of Basrah, Basrah, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.6.28

Keywords:

q-difference equation, generating function, Rogers formula, Mehler’s formula, homogeneous q-shift operator, Srivastava-Agarwal type generating function

Abstract

This paper concentrates on employing the -difference equations approach to prove another generating function, extended generating function, Rogers formula and Mehler’s formula for the polynomials , as well as thegenerating functions of Srivastava-Agarwal type. Furthermore, we establish links between the homogeneous -difference equations and transformation formulas.