Uniform asymptotics of orthogonal polynomials arising from Coherent states

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Article numberA070
Journal / PublicationSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Online published31 Aug 2015
Publication statusPublished - 2015


In this paper, we study a family of orthogonal polynomials {φ(z)} arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of φ(z) as the polynomial degree n tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong’s difference equation method. In addition, the limiting zero distribution of the polynomials φ(z) is provided.

Research Area(s)

  • Coherent states, Orthogonal polynomials, Three-term recurrence relation, Uniform asymptotics