Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure

2015/04/22 by Alfredo Deaño, Deaño, Alfredo, Edmundo J. Huertas +3
Mathematics · Physics and Astronomy · #33C15 #33C45 #41A60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math.CA #msc:33C15 #msc:33C45 #msc:41A60

paper · pdf · doi:10.48550/arxiv.1504.05976

17 pages, no figures

arxiv created 2015/04/22 · openalex publication_date 2015/04/22 · arxiv updated 2015/04/24 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure: (1)/(x-c)x^αe^-xdx+Nδ(x-c), for x∈[0,∞), α>-1, a free parameter N∈ ℝ₊ and a shift c<0. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as n tends to infinity.

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