<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

On generalized Laguerre matrix polynomials

Department of Mathematics, Faculty of Science

Department of Mathematics, Faculty of Education

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On generalized Laguerre matrix polynomials"}

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...

On generalized Laguerre matrix polynomials

Publié en ligne: 10 sept. 2018

Pages: 32 - 45

Reçu: 05 janv. 2015

DOI: https://doi.org/10.2478/ausm-2018-0003

Mots clés
Laguerre matrix polynomials, three terms recurrence relation, generalized hypergeometric matrix function and Gamma matrix function

© 2018 Raed S. Batahan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On generalized Laguerre matrix polynomials

Publié en ligne: 10 sept. 2018

Pages: 32 - 45

Reçu: 05 janv. 2015

DOI: https://doi.org/10.2478/ausm-2018-0003

Mots clésLaguerre matrix polynomials, three terms recurrence relation, generalized hypergeometric matrix function and Gamma matrix function

© 2018 Raed S. Batahan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Laguerre matrix polynomials, three terms recurrence relation, generalized hypergeometric matrix function and Gamma matrix function