Monotonicity of Zeros of Jacobi-Angelesco polynomials
Eliel J. C. dos Santos

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 and . We prove that the zeros are monotonic functions of and and consider some special cases of how the zeros depend on , 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.
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Taxonomy
TopicsMathematical functions and polynomials · Iterative Methods for Nonlinear Equations · Advanced Mathematical Identities
