Generalized Form of Hermite Matrix Polynomials via the Hypergeometric Matrix Function ()

Raed S. Batahan

Department of Mathematics, Faculty of Science, Hadhramout University, Hadhranout, Yemen.

**DOI: **10.4236/alamt.2014.42012
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Department of Mathematics, Faculty of Science, Hadhramout University, Hadhranout, Yemen.

The object of this paper is to present a new generalization of the Hermite matrix polynomials by means of the hypergeometric matrix function. An integral representation, differential recurrence relation and some other properties of these generalized forms are established here. Moreover, some new properties of the Hermite and Chebyshev matrix polynomials are obtained. In particular, the two-variable and two-index Chebyshev matrix polynomials of two matrices are presented.

Keywords

Hermite and Chebyshev Matrix Polynomials, Three Terms Recurrence Relation, Hypergeometric Matrix Function and Gamma Matrix Function

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Batahan, R. (2014) Generalized Form of Hermite Matrix Polynomials via the Hypergeometric Matrix Function. *Advances in Linear Algebra & Matrix Theory*, **4**, 134-141. doi: 10.4236/alamt.2014.42012.

Conflicts of Interest

The authors declare no conflicts of interest.

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