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

摘要

We propose to define the Horn's double hypergeometric functions H3 and H_4 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 H_A and H_B 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 results of Choi, Hasanov and Turaev (Choi, Junesang, Hasanov, Anvar and Turaev, Mamasali, Integral representations for Srivastava's hypergeometric function H_B, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., Vol. 19, No. 2 (May 2012), (2012), 137-145: http://dx.doi.org/10.7468/jksmeb.2012.19.2.137; Choi, Junesang, Hasanov, Anvar and Turaev, Mamasali, Integral representations for Srivastava's hypergeometric function H_A, Honam Mathematical J., Vol. 34, No. 1, (2012), 113-124: http://dx.doi.org/10.5831/HMJ.2012.34.1.113; Choi, Junesang, Hasanov, Anvar and Turaev, Mamasali