Geodesic
On Hermite-Hermite matrix polynomials
Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 421-434

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MR Zbl
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.
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.
DOI : 10.21136/MB.2008.140630
Classification : 15A16, 15A54, 15A60, 33C05, 33C45
Keywords: matrix functions; Hermite matrix polynomials; recurrence relation; Hermite matrix differential equation; Rodrigues's formula 
Metwally, M. S.; Mohamed, M. T.; Shehata, A. On Hermite-Hermite matrix polynomials. Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 421-434. doi: 10.21136/MB.2008.140630
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