Plancherel-Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems

    Authors

    D. Dai; M. E. H. Ismail;X. S. Wang

    Comments

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    Abbreviated Journal Title

    Constr. Approx.

    Keywords

    Asymptotics; The Chen-Ismail polynomials; The Berg-Letessier-Valent; polynomials; The Conrad-Flajolet polynomials; Turning points; Difference; equation technique; Indeterminate moment problems; Nevanlinna functions; Asymptotics of zeros; Plancherel-Rotach asymptotics; VARYING RECURRENCE COEFFICIENTS; LINEAR DIFFERENCE-EQUATIONS; ORTHOGONAL; POLYNOMIALS; WEIGHTS; RESPECT; Mathematics

    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.

    Journal Title

    Constructive Approximation

    Volume

    40

    Issue/Number

    1

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    61

    Last Page

    104

    WOS Identifier

    WOS:000339401100003

    ISSN

    0176-4276

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