Recursion formulas of q-Appell functions

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.