Title

Plancherel-Rotach Asymptotic Expansion For Some Polynomials From Indeterminate Moment Problems

Keywords

Asymptotics; Asymptotics of zeros; Difference equation technique; Indeterminate moment problems; Nevanlinna functions; Plancherel-Rotach asymptotics; The Berg-Letessier-Valent polynomials; The Chen-Ismail polynomials; The Conrad-Flajolet polynomials; Turning points

Abstract

We study the Plancherel-Rotach asymptotics of four families of orthogonal polynomials: the Chen-Ismail polynomials, the Berg-Letessier-Valent polynomials, and the Conrad-Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems, and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems. © 2013 Springer Science+Business Media New York.

Publication Date

8-1-2014

Publication Title

Constructive Approximation

Volume

40

Issue

1

Number of Pages

61-104

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00365-013-9215-1

Socpus ID

84904247285 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84904247285

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