On the integral representations of some of the Horn’s double and Srivastava’s triple hypergeometric functions of matrix arguments ∗

Lalit Mohan Upadhyaya; Ayman Shehata; A Kamal

doi:10.48165/

Authors

Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand-248179, India.
Ayman Shehata Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt.
A Kamal Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt

DOI:

https://doi.org/10.48165/

Keywords:

representations, hypergeometric, functions, matrix argument

Abstract

We propose to define the Horn’s double hypergeometric functions H3 and H4 of matrix arguments and deduce some integral representations for these two functions. Utilizing the first author’s definitions (Upadhyaya, Lalit Mohan and Dhami, H.S., Matrix generalizations of multiple hypergeometric functions; #1818, Nov.2001, IMA Preprint Series, University of Minnesota, Minneapolis, U.S.A. (Retrieved from the University of Minnesota Digital Conservancy, http://hdl.handle.net/11299/3706); Upadhyaya, Lalit Mohan, Matrix Generalizations of Multiple Hypergeometric Functions by Using Mathai’s Matrix Transform Techniques (Ph.D. Thesis, Kumaun University, Nainital, Uttarakhand, India), #1943, Nov. 2003, IMA Preprint Series, University of Minnesota, Minneapolis, U.S.A. ( https://www.ima.umn.edu/sites/default/files/1943.pdf http://www.ima.umn.edu/preprints/abstracts/1943ab.pdfhttp://www.ima.umn.edu/ preprints/nov2003/1943.pdf http://hdl.handle.net/11299/3955 https://zbmath.org/?q=an:1254.33008 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.2172\&rank=52). (Retrieved from the University of Minnesota Digital Conservancy, http://hdl.handle. net/11299/3955)) of the Srivastava’s triple hypergeometric functions HA and HB of matrix arguments, we further establish a number of integral representations for these two Srivastava’s triple hypergeometric functions, which generalize some of the recent

References

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Bulletin of Pure and Applied Sciences Section E - Mathematics & Statistics, Vol. 39 E, No. 1, January-June, 2020

Lalit Mohan Upadhyaya, Ayman Shehata and A. Kamal

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