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A new kind of Legendre matrix polynomials

Research Authors
Ayman Shehata
Research 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.

Research Department
Research Journal
Gazi University Journal of Science
Research Publisher
2016
Research Rank
1
Research Vol
Vol. 29, No. 2
Research Website
http://gujs.gazi.edu.tr/article/view/5000129499
Research Year
2016
Research Pages
535-558