Constructive Approximation

, Volume 22, Issue 2, pp 255–271 | Cite as

Structural Formulas for Orthogonal Matrix Polynomials Satisfying Second-Order Differential Equations, I

Article

Abstract

We develop structural formulas satisfied by some families of orthogonal matrix polynomials of size $2\times 2$ satisfying second-order differential equations with polynomial coefficients. We consider here two one-parametric families of weight matrices, namely \[ H_{a,1}(t)\;=\;e^{-t^2} \left( \begin{array}{@{}cc@{}} 1+\vert a\vert ^2t^2 & at \\ \bar at & 1 \end{array} \right) \quad {\rm and} \quad H_{a,2}(t)\;=\;e^{-t^2} \left( \begin{array} {@{}cc@{}} 1+\vert a\vert ^2t^4 & at^2 \\ \bar at^2 & 1 \end{array} \right), \] $a\in \mbox{\bf C} $ and $t\in \mbox{\bf R} $, and their corresponding orthogonal polynomials.

Orthogonal polynomials Matrix orthogonality Rodriques’ formulas Generating functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Universidad de Sevilla, Afdo (P.O. Box) 1160, H1080 SevillaSpain

Personalised recommendations