title: The q-Laguerre matrix polynomials.
abstract: The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable. Four generating functions of this matrix polynomials are investigated. Two slightly different explicit forms are introduced. Three-term recurrence relation, Rodrigues-type formula and the q-orthogonality property are given.
authors.affiliation: Department of Basic Science, Faculty of Information Systems and Computer Science, October 6 University, Sixth of October City, Egypt.
authors.forename: Ahmed
authors.initials: A
authors.lastname: Salem
keywords: Matrix functional calculus; Rodrigues-type formula; Three terms recurrence relation; q-Gamma matrix function; q-Laguerre matrix polynomials