Using orthogonal polynomials, we give a different approach to some recent results on tridi-agonal matrices. 1. Introduction and preliminaries. Most of the results on tridiagonal matrices can be seen in the context of orthogonal polynomials. Here, we will see two examples. The aim of this note is to give simplified proofs of some recent results on tridiagonal matrices , using arguments from the ...

Multiple orthogonal polynomials are polynomials of one variable that satisfy orthogonality conditions with respect to several measures. They are a very useful extension of orthogonal polynomials and recently received renewed interest because tools have become available to investigate their asymptotic behavior. They appear in rational approximation, number theory, random matrices, integrable sys...

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, ...

In this paper we investigate connection between semi-integer orthogonal polynomials and Szegő’s class of polynomials, orthogonal on the unit circle. We find a representation of the semi-integer orthogonal polynomials in terms of Szegő’s polynomials orthogonal on the unit circle for certain class of weight functions.

It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent polynomials on the unit circle. More precisely, it is a consequence of the five term recurrence relation obtained for these orthogonal Laurent polynomials, and the ...