A note on two variable Laguerre matrix polynomials

Abstract

The principal object of this paper is to present a natural further step toward the mathematical properties and presentations concerning the two variable Laguerre matrix polynomials defined in (Bin-Saad, Maged G., Antar, A. Al-Sayaad, 2015. Study of two variable Laguerre polynomials via symbolic operational images. Asian J. of math. and comput. research, 2(1), 42-50). Series expansions, integral transforms and bilinear and bilateral generating matrix functions for these polynomials are established. Some particular cases and consequences of our main results are also considered.

Two Variables Shivley’s Matrix Polynomials

“…In [9,10], Subuhi Khan and others introduced the 2-variable forms of Laguerre and modified Laguerre matrix polynomials and generalized Hermite matrix based polynomials of two variables and Lie algebraic techniques. Furthermore, several papers concerning the orthogonal matrix polynomials for two and multivariables have become more and more relevant, see for example [11][12][13][14][15][16][17].…”

Lie algebra and Laguerre Matrix Polynomials of One Variable

“…The analogous extension to the matrix framework for the classical case of Laguerre, modified Laguerre, and LaguerreKonhauser matrix polynomials have been studied in [1,4,6,7,9,11,12,14,15,16,17,18]. Indeed, in recent papers, Laguerre matrix polynomials have significant emergent.…”

Lie algebra and Laguerre Matrix Polynomials of One Variable

“…The analogous extension to the matrix framework for the classical case of Laguerre, modified Laguerre, and Laguerre-Konhauser matrix polynomials have been studied in [1,4,6,7,9,11,12,14,15,16,17,18]. Indeed, in recent papers, Laguerre matrix polynomials have significant emergent.…”