Abstract
In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansions of the Humbert matrix polynomials of two variables in series of Hermite polynomials are given. Results of Gegenbauer ma-trix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables.
Highlights
The special matrix functions appear in statistics, lie group theory and number theory [1,2,3,4] and the matrix polynomials have become more important and some results in the theory of classical orthogonal polynomials have been extended to orthogonal matrix polynomials see for instance [5,6,7,8,9].If D0 is the complex plane cut along the negative, real axis and log z denotes the principal logarithm of z
In this paper we introduce Humbert matrix polynomials of two variables
Results of Gegenbauer matrix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables
Summary
The special matrix functions appear in statistics, lie group theory and number theory [1,2,3,4] and the matrix polynomials have become more important and some results in the theory of classical orthogonal polynomials have been extended to orthogonal matrix polynomials see for instance [5,6,7,8,9]. Re z 0 for all z A
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