Recursion formulas of q-Appell functions

TL;DR

This paper derives recursion formulas for q-Appell functions, extending known relations of classical Appell functions to their q-analogues, thereby enriching the theory of hypergeometric functions.

Contribution

It introduces recursion formulas for q-Appell functions as q-analogues of classical Appell function relations, expanding the mathematical framework of hypergeometric series.

Findings

Recursion formulas for q-Appell functions $\

, , , $ are established.

The formulas serve as q-analogues of classical Appell function relations.

Abstract

Recently, Opps, Saad and Srivastava gave the recursion formulas of Appell's function F2. The first author of this paper then established the recursion formulas for Appell functions F1, F2, F3 and F4 by the contiguous relations of hypergeometric series. In this paper, the authors will present the recursion formulas for q-Appell functions $\Phi^{(1)}, \Phi^{(2)}, \Phi^{(3)}$ and $\Phi^{(4)}$ as the q-analogies of F1, F2, F3 and F4's relations.