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Euler-type integrals for the generalized hypergeometric matrix function

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Veröffentlicht/Copyright: 25. August 2023

Abstract

The special matrix functions have received significant attention in many fields, such as theoretical physics, number theory, probability theory, and the theory of group representations. In 2017, Dwivedi and Sahai introduced the generalized hypergeometric matrix function using matrix parameters and proved the convergence on | z | = 1 . Recently, hypergeometric matrix functions and their potential applications have played a major role in mathematical physics and engineering. Motivated by aforesaid works and in order to enrich this flourishing field, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and determine various transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have been provided for several particular cases.


Dedicated to my daughter Vamsi Pal on her second birthday


Acknowledgements

The authors would like to thank the referees for their insightful comments and suggestions, which led to a better presentation of the paper.

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Received: 2023-04-11
Revised: 2023-07-28
Accepted: 2023-07-28
Published Online: 2023-08-25
Published in Print: 2023-12-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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