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...

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.