A novel Beta matrix function via Wiman matrix function and their applications

Abstract

Many authors defined and extended the beta function in various forms because the beta function has wide uses in different fields of science and applied science. In this article, we define a new more generalized form of the extended beta matrix function via the Wiman matrix function and describe their significant properties and special cases. Furthermore, we define an extension of the Gauss hypergeometric and confluent hypergeometric matrix functions by adopting a novel type of beta matrix function. We also derive their Laplace transform, derivative formula and transformation formulae.