Ratio asymptotic for bi-orthogonal matrix polynomials with unbounded recurrence coefficients

TL;DR

This paper investigates the ratio asymptotic behavior of matrix biorthogonal polynomials with unbounded recurrence coefficients, providing general results and illustrative examples.

Contribution

It derives the ratio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients under broad conditions.

Findings

Established ratio asymptotics for the polynomials

Provided illustrative examples demonstrating the theory

Extended understanding of biorthogonal polynomial behavior

Abstract

In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived in quite general assumptions. It is considered some illustrative examples.