# Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class

## TL;DR

This paper investigates the limiting behavior of recurrence coefficients for multiple orthogonal polynomials in a Nevai class, describing their limits via differential equations and illustrating results numerically for Angelesco systems.

## Contribution

It introduces a novel approach to characterize the limits of recurrence coefficients using differential equations for multiple orthogonal polynomials in a Nevai class.

## Key findings

- Limits of recurrence coefficients are described by PDEs or ODEs.
- Numerical illustrations are provided for Angelesco systems.
- The approach advances understanding of asymptotic properties of multiple orthogonal polynomials.

## Abstract

A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighbor coefficients have a limit along rays of the lattice, we describe it in terms of the solution of a system of partial differential equations. In the case of two orthogonality measures the differential equation becomes ordinary. For Angelesco systems, the result is illustrated numerically.