Abstract
The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.
Highlights
In the last two decade, 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 [1]-[7]
Orthogonal matrix polynomials are important from both the theoretical and practical points of view, they appear in connection with representation theory, matrix expansion problems, prediction theory and in the matrix quadrature integration problems, see for example [5] [8] [9]
Physics and mechanics are related to second order matrix differential equation
Summary
In the last two decade, 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 [1]-[7]. We construct a matrix version of the pseudo Laguerre matrix polynomials given by (1.4) as follows: Definition 1.1. We define the pseudo-Laguerre matrix polynomials by the series ( ) = Ln ( x, y; k, A). We must emphasize that the matrix polynomials in (1.6) are a generalized form of Konhauser matrix polynomials defined by (1.3) and we have. Kampé de Fériet double hypergeometric series [ ] F p:q;k l:m;n x, y and matrix version of the generalized hypergeometric function p Fq [24] as follows:
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