Recursion formulas for the Srivastava–Daoust and related multivariable hypergeometric functions

Abstract

This paper concludes the study of recursion formulas of multivariable hypergeometric functions. Earlier in [V. Sahai and A. Verma, Recursion formulas for multivariable hypergeometric functions, Asian–Eur. J. Math. 8 (2015) 50, 1550082], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava’s triple hypergeometric functions and [Formula: see text]-variable Lauricella functions. Further, in [V. Sahai and A. Verma, Recursion formulas for Recursion formulas for Srivastava’s general triple hypergeometric functions, Asian–Eur. J. Math. 9 (2016) 17, 1650063], we have obtained recursion formulas for Srivastava general triple hypergeometric function [Formula: see text]. We present here the recursion formulas for generalized Kampé de Fériet series and Srivastava and Daoust multivariable hypergeometric function. Certain particular cases leading to recursion formulas of certain generalized hypergeometric function of one variable, certain Horn series, Humbert’s confluent hypergeometric series and some confluent forms of Lauricella series in [Formula: see text]-variables are also presented.