2023/10/10 by Andrei Martı́nez-Finkelshtein, Martinez-Finkelshtein, Andrei, R. Morales +1
Mathematics · Physics and Astronomy · #33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2310.06688
openalex publication_date 2023/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Information about the behavior of zeros of classical families of multiple or Hermite-Padé orthogonal polynomials as functions of the intrinsic parameters of the family is scarce. We establish the interlacing properties of the zeros of Angelesco-Jacobi polynomials when one of the three main parameters is increased by 1, extending the work of dos Santos (2017). We also show their monotonicity with respect to (large values) of the parameter representing in the electrostatic model of the zeros the size of the positive charge fixed at the origin, as well as monotonicity with respect to the endpoint of the interval of orthogonality. These results are extended to zeros of multiple Jacobi-Laguerre and Laguerre-Hermite polynomials using asymptotic relations between these families.