On some generalizations of the beta function in several variables

Authors

MUSTAPHA RAISSOULI
SALMA EL-SOUBHY

DOI

10.3906/mat-2010-57

Abstract

Intensive studies aiming to extend the gamma and beta functions and to establish some properties for these extensions 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. Among others, we investigate recurrence relationships, Mellin transform properties, and partial differential equations involving these generalized functions. At the end, some results about partial derivatives of these extended functions are presented as well.

Keywords

Beta function, gamma function, beta function in n variables, extended beta function in n variables, generalized beta function in n variables

First Page

820

Last Page

842

Recommended Citation

RAISSOULI, MUSTAPHA and EL-SOUBHY, SALMA (2021) "On some generalizations of the beta function in several variables," Turkish Journal of Mathematics: Vol. 45: No. 2, Article 12. https://doi.org/10.3906/mat-2010-57
Available at: https://journals.tubitak.gov.tr/math/vol45/iss2/12