Asymptotic Properties of Some Freud Polynomials

2023/08/07 by Chao Min, Liwei Wang, Min, Chao +3
Mathematics · Physics and Astronomy · #33C45 #41A60 #42C05 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2308.03246

openalex publication_date 2023/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial leading coefficients of the monic OPs, the associated Hankel determinants and the squares of L²-norm of the monic OPs. These results are derived from the combination of the ladder operator approach, Dyson's Coulomb fluid approach and some recent results in the literature.

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