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MATHEMATICA BOHEMICA, Vol. 133, No. 4, pp. 421-434 (2008)
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On Hermite-Hermite matrix polynomials

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M. S. Metwally, M. T. Mohamed, A. Shehata

* M. S. Metwally*, * M. T. Mohamed*, * A. Shehata*, Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt, e-mail: {\tt 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 (MSC2000):** 15A60, 33C05, 33C45

**Full text of the article:**

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