On some generalizations of the beta function in several variables

Abstract

Intensive studies aiming to extend the gamma and beta functions and to establish some properties for theseextensions have been recently carried out. In this paper, we first introduce a generalized gamma function in n variables.Afterwards, two generalized beta functions in several variables are introduced and their properties are discussed. Amongothers, we investigate recurrence relationships, Mellin transform properties, and partial differential equations involvingthese generalized functions. At the end, some results about partial derivatives of these extended functions are presentedas well.