On generalized Laguerre matrix polynomials. (English) Zbl 1315.15020

Batahan, Raed S.; Bathanya, A. A.

Acta Univ. Sapientiae, Math. 6, No. 2, 121-134 (2014).

Summary: The main object of the present paper is to introduce and study the generalized Laguerre matrix polynomials for a matrix that satisfies an appropriate spectral property. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, integral expression and some recurrence relations in particular the three terms recurrence relation are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.

MSC:

15A54	Matrices over function rings in one or more variables
15A16	Matrix exponential and similar functions of matrices
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Laguerre matrix polynomials; three terms recurrence relation; generalized hypergeometric matrix function and gamma matrix function

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