Some results of new extended beta, hypergeometric, Appell and Lauricella matrix functions

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.

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

Khan

Husain

2023

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Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions

Verma,

Yadav,

Sharan

et al. 2024

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In this paper, we investigate the matrix analogues of the Ψ-beta and Ψ-gamma functions, as well as their properties. With the help of the Ψ-beta matrix function (BMF), we introduce the Ψ-Gauss hypergeometric matrix function (GHMF) and the Ψ-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the Ψ-Appell and the Ψ-Lauricella matrix functions are defined by applications of the Ψ-BMF, and their integral representations are also given.

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Some results of new extended beta, hypergeometric, Appell and Lauricella matrix functions

Cited by 2 publications

References 28 publications

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

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

Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions

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