Zeros of entire functions and a problem of Ramanujan

    Authors

    M. E. H. Ismail;C. G. Zhang

    Comments

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    Abbreviated Journal Title

    Adv. Math.

    Keywords

    Stieltjes-Wigert polynomials; q-Airy function; Ramanujan's entire; function; q-Bessel functions; q-Laguerre polynomials; asymptotics; recurrence relations; zeros; STIELTJES-WIGERT POLYNOMIALS; ORTHOGONAL POLYNOMIALS; BESSEL-FUNCTIONS; ASYMPTOTICS; Mathematics

    Abstract

    We derive representations for certain entire q-functions and apply our technique to the Ramanujan entire function (or q-Airy function) and q-Bessel functions. This is used to show that the asymptotic series of the large zeros of the Ramanujan entire function and similar functions are also convergent series. The idea is to show that the zeros of the functions under consideration satisfy a nonlinear integral equation. (c) 2006 Elsevier Inc. All rights reserved.

    Journal Title

    Advances in Mathematics

    Volume

    209

    Issue/Number

    1

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    363

    Last Page

    380

    WOS Identifier

    WOS:000244218000010

    ISSN

    0001-8708

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