1Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, 248179, India
2Department of Mathematics, Faculty of Science, Assiut University, Assiut, 1516, Egypt
3Department of Mathematics, College of Science and Arts in Unaizah, Qassim University, Qassim, 10363, Kingdom of Saudi Arabia. Email: drshehata2006@yahoo.com
*Corresponding Author: Lalit Mohan Upadhyaya, Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, 248179, India. Email: lmupadhyaya@rediffmail.com
2010 AMS Mathematics Subject Classification: Primary: 33C05, 33C10, 33C15, 33C20, 33C99 Secondary: 60E, 62H, 44A05.
We prove some Eulerian integrals involving the hypergeometric functions of single matrix argument. The integrals studied here involve the 0F1, 1F2, 2F3, 1F1, 3F3, 2F1 and the 3F2 functions of matrix argument. We apply the Mathai's matrix transform technique to prove our results which provide a generalization of the corresponding results available in the literature for these functions for the case of scalar variables. At the end we also give the corresponding results when the argument matrices are complex Hermitian positive definite.
Hypergeometric functions, matrix argument, matrix transform, real positive definite, Hermitian positive definite
