Monotonicity of Zeros of Jacobi-Angelesco polynomials

TL;DR

This paper investigates how the zeros of Jacobi-Angelesco polynomials change with parameters, establishing monotonicity properties and extending results to related orthogonal polynomial families.

Contribution

It proves the monotonicity of zeros with respect to parameters for Jacobi-Angelesco polynomials and explores implications for related polynomial families.

Findings

Zeros are monotonic functions of parameters α and γ.

Monotonicity results extend to Jacobi-Laguerre and Laguerre-Hermite polynomials.

Special cases reveal symmetry effects on zero behavior.

Abstract

We study the monotonic behaviour of the zeros of the multiple Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to the parameters $\alpha,\beta$ and $\gamma$. We prove that the zeros are monotonic functions of $\alpha$ and $\gamma$ and consider some special cases of how the zeros depend on $\beta$, especially in the presence of symmetry. As a consequence we obtain results about monotonicity of zeros of Jacobi-Laguerre and Laguerre-Hermite multiple orthogonal polynomials too.