Bulletin of Pure & Applied Sciences- Mathematics and Statistics

  • Year: 2020
  • Volume: 39e
  • Issue: 2

On the Exton’s triple hypergeometric function X2 of matrix argum*

  • Author:
  • Lalit Mohan Upadhyaya1, Ayman Shehata2, A. Kamal3
  • Total Page Count: 13
  • Published Online: Aug 30, 2021
  • Page Number: 289 to 301

1. Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand-248179, India.

2. Department of Mathematics, Faculty of Science, Assiut University, Assiut71516, Egypt., Department of Mathematics, College of Science and Arts at Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia.

3. Department of Mathematics, College of Science and Arts at Muthnib, Qassim University, Qassim, Kingdom of Saudi Arabia., Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt.

†Corresponding author Lalit Mohan Upadhyaya, E-mail: lmupadhyaya@rediffmail.com, hetchres@gmail.com

2. E-mail: drshehata2006@yahoo.com

3. E-mail: alaa_mohamed1@yahoo.com

Abstract

We define the Exton’s triple hypergeometric function X2 of matrix arguments and establish some integral representations for this function which generalize the corresponding results of Choi, Hasanov and Turaev (Choi, Junesang, Hasanov, Anvar and Turaev, Mamasali, Certain integral representations of Euler type for the Exton function X2, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 17(4), (2010), 347–354) for the matrix arguments case.

Keywords

Hypergeometric functions, Exton’s triple hypergeometric function, Matrix argument, Matrix transform, Real positive definite, Hermitian positive definite