Some relations satisfied by orthogonal matrix polynomials. (English) Zbl 1229.33012

Çekim, Bayram; Altın, Abdulla; Aktaş, Rabia

Hacet. J. Math. Stat. 40, No. 2, 241-253 (2011).

Summary: The main purpose of this paper is to obtain some properties of orthogonal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Furthermore, for these matrix polynomials, we give raising operators.

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
15A60	Norms of matrices, numerical range, applications of functional analysis to matrix theory

Keywords:

Laguerre matrix polynomials; Hermite matrix polynomials; Gegenbauer matrix polynomials; power series; raising operator