On a multivariable extension of Jacobi matrix polynomials

Tasdelen F., ÇEKİM B., AKTAŞ R.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.61, no.9, pp.2412-2423, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 9
  • Publication Date: 2011
  • Doi Number: 10.1016/j.camwa.2011.02.019
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2412-2423
  • Keywords: Jacobi matrix polynomials, Generating matrix function, Recurrence relation, Multilinear and multilateral generating matrix functions, DIFFERENTIAL-EQUATIONS, ORTHOGONAL POLYNOMIALS
  • Gazi University Affiliated: Yes

Abstract

The classical Jacobi matrix polynomials only for commutative matrices were first studied by Defez et al. [E. Defez, L. Jodar, A. Law. Jacobi matrix differential equation, polynomial solutions and their properties, Comput. Math. Appl. 48 (2004) 789-803]. The main aim of this paper is to construct a multivariable extension with the help of the classical Jacobi matrix polynomials (JMPs). Generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived. Furthermore, general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented. (C) 2011 Elsevier Ltd. All rights reserved.