Title

Zeros of entire functions and a problem of Ramanujan

Authors

Authors

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

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

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

Share

COinS