Ratio asymptotics for multiple orthogonal polynomials

TL;DR

This paper investigates the asymptotic behavior of ratios of neighboring multiple orthogonal polynomials, assuming the convergence of recurrence coefficients, providing insights into their long-term behavior.

Contribution

It establishes the ratio asymptotics for multiple orthogonal polynomials under recurrence coefficient convergence, advancing understanding in this area.

Findings

Derived asymptotic formulas for polynomial ratios

Connected recurrence coefficient convergence to polynomial behavior

Enhanced theoretical understanding of multiple orthogonal polynomials

Abstract

We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the recurrence coefficients in the nearest neighbor recurrence relations converge.