Mathematica Bohemica, Vol. 141, No. 4, pp. 407-429, 2016
Some relations on Humbert matrix polynomials
Ayman Shehata
Received February 18, 2014. First published August 2, 2016.
Abstract: The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.
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Affiliations: Ayman Shehata, Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt, and Department of Mathematics, College of Science and Arts, Qassim University, King Abdulaziz Road, Unaizah, Qassim 10363, Kingdom of Saudi Arabia, e-mail: drshehata2006@yahoo.com
