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M. S. Metwally, M. T. Mohamed, A. Shehata, Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt, e-mail: m$_-$ayman2004 @yahoo.com, Kamel702007@yahoo.com
Abstract: 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.
Keywords: matrix functions, Hermite matrix polynomials, recurrence relation, Hermite matrix differential equation, Rodrigues's formula
Classification (MSC 2000): 15A60, 33C05, 33C45
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