Generalization of Gamma and Beta Functions with Certain Properties and Statistical Application

Maryam K. Rasheed; Abdulrahman H. Majeed

doi:10.24996/ijs.2023.64.7.36

Authors

Maryam K. Rasheed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-0811-9925
Abdulrahman H. Majeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.7.36

Keywords:

Gamma functoin, Beta function, Integral representation, Mellin transform, Beta distribution

Abstract

This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.