A NEW KIND OF LEGENDRE MATRIX POLYNOMIALS

Abstract

The main aim of this paper is to introduce a new kind of Legendre matrix polynomials. Hypergeometric matrix representation of these matrix polynomials is given. The convergence properties and the integral form for the Legendre matrix polynomials are derived. The Legendre matrix differential equation of second order is established. Subsequently, Rodrigues formula, orthogonality property, matrix recurrence relation and types of generating matrix functions are then developed for the Legendre matrix polynomials. Furthermore, general families of bilinear and bilateral generating matrix functions for these matrix polynomials are obtained and their applications are presented. Finally, the composite Legendre matrix polynomials is introduced.

Keywords

• ypergeometric matrix function,Legendre matrix polynomials; Legendre matrix differential equations; Rodrigues formula; Orthogonality; Matrix recurrence relation; Generating matrix functions

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