Basic completely monotone functions as coefficients and solutions of linear q-difference equations with some applications

Abstract

This paper is devoted to give some properties of the q derivatives of basic hypergeometric series with respect to parameters. The q derivatives of the basic hypergeometric functions with respect to parameters are employed to show and explain some properties of the solutions of q-difference equations with basic completely monotone functions as coefficients. As an application, some physical problems related to Jacobi Theta functions and its q derivatives are illustrated