Some new asymptotic properties for the zeros of Jacobi, Laguerre and\n Hermite polynomials

1994/06/06 by Holger Dette, Dette, Holger, W. J. Studden +1 · 3 citations
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.math/9406224

openalex publication_date 1994/06/06 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

For the generalized Jacobi, Laguerre and Hermite polynomials P_n^{(\α_n,\n\β_n)} (x), L_n^(\α_n) (x), break H_n^(\γ_n) (x) the limit\ndistributions of the zeros are found, when the sequences \α_n or\n\β_n tend to infinity with a larger order than n. The derivation uses\nspecial properties of the sequences in the corresponding recurrence formulae.\nThe results are used to give second order approximations for the largest and\nsmallest zero which improve (and generalize) the limit statements in a paper of\nMoak, Saff and Varga [11].\n

Cited by

• Zero distribution of multiplicative Hermite and Laguerre polynomials
• Finite free probability and S transforms of Jacobi processes
• Zeros and exponential profiles of polynomials II: Examples

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