Displaying similar documents to “Gegenbauer matrix polynomials and second order matrix differential equations.”

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...

Integral representations for multiple Hermite and multiple Laguerre polynomials

Pavel M. BLEHER, Arno B.J. Kuijlaars (2005)

Annales de l’institut Fourier

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We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.