Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

    Authors

    M. E. H. Ismail;X. Li

    Comments

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    Abbreviated Journal Title

    Constr. Approx.

    Keywords

    q-Orthogonal polynomials; Asymptotics; Recurrence relations; Ramanujan; function; Error terms; VARYING RECURRENCE COEFFICIENTS; Mathematics

    Abstract

    We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q (-1)-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function.

    Journal Title

    Constructive Approximation

    Volume

    37

    Issue/Number

    3

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    341

    Last Page

    356

    WOS Identifier

    WOS:000319021000002

    ISSN

    0176-4276

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