Recurrence relations of the multiple hypergeometric function of Srivastava and Daoust and the multivariable H-function of Srivastava and Panda
The authors begin by deriving several multiple integral representations for the generalized Lauricella hypergeometric function of several variables, which was introduced and studied (almost two decades ago) by the reviewer and \textit{M. C. Daoust} [Indagationes Math. 31, 449-457 (1969; Zbl 0185.298)]. Making use of these integral representations, they deduce various recurrence relations for the Srivastava-Daoust multivariable hypergeometric function, and also for the H-function of several variables, introduced and studied by the reviewer and \textit{R. Panda} [J. Reinge Angew. Math. 283/284, 265-274 (1976; Zbl 0315.33003); ibid. 288, 129-145 (1976; Zbl 0326.33004)]. Each of the aforementioned multivariable functions has been considered, among other places, in a monograph on the subject by the reviewer, \textit{K. C. Gupta} and \textit{S. P. Goyal} [The H-functions of one and two variables with applications (1982; Zbl 0506.33007)].
Lauricella hypergeometric function of several variables
scientific article; zbMATH DE number 3993989