Displaying similar documents to “On generalized Hermite matrix polynomials.”

On Hermite-Hermite matrix polynomials

M. S. Metwally, M. T. Mohamed, A. Shehata (2008)

Mathematica Bohemica

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In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite matrix polynomials is proposed.

Some relations on Humbert matrix polynomials

Ayman Shehata (2016)

Mathematica Bohemica

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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...

Some relations satisfied by Hermite-Hermite matrix polynomials

Ayman Shehata, Lalit Mohan Upadhyaya (2017)

Mathematica Bohemica

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The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the...