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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2019, Volume & Issue : BPAS-Maths & Stat 38E(1), JAN-JUN 2019
Page No. : 159-170, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2019.00014.6 (Received on 12.11.2018, Revised on 26.03.2019, Accepted on 07.04.2019)

ON THE SRIVASTAVA’S FUNCTION ${H_B}$ OF MATRIX ARGUMENTS’

Lalit Mohan Upadhyaya1,*, Ayman Shehata2
Author’s Affiliation : 1Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand 248179, India. E-mail: [email protected], [email protected] 2 Department of Mathematics, Faculty of Science, Assiut University, Assiut 1516, Egypt. 2 Department of Mathematics, College of Science and Arts in Unaizah, Qassim University, Qassim 10363, Kingdom of Saudi Arabia. E-mail: [email protected]

Corresponding Author : Lalit Mohan Upadhyaya, Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand 248179, India.,
E-Mail:-[email protected], [email protected]


Abstract

We establish some integral representations for the Srivastava’s triple hypergeometric function ${H_B}$ of matrix arguments which generalize some of the recent results of Choi, Hasanov and Turaev [12] for this function. We prove our results by employing the Mathai’s matrix transform technique for real symmetric positive definite matrices as arguments. Towards the end of the paper we also give the corresponding results when the argument matrices are complex Hermitian positive definite.

2010 AMS Mathematics Subject Classification: Primary:  33C05, 33C10, 33C15, 33C20, 33C99

                                                                                              Secondary:  60E, 62H, 44A05.

Keywords

hypergeometric functions, Srivastava’s triple hypergeometric functions, Exton’s triple hypergeometric function, matrix argument, matrix transform, real positive definite, Hermitian positive definite.
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