Title
Zeros Of Entire Functions And A Problem Of Ramanujan
Keywords
Asymptotics; q-Airy function; q-Bessel functions; q-Laguerre polynomials; Ramanujan's entire function; Recurrence relations; Stieltjes-Wigert polynomials; Zeros
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. © 2006 Elsevier Inc. All rights reserved.
Publication Date
2-15-2007
Publication Title
Advances in Mathematics
Volume
209
Issue
1
Number of Pages
363-380
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.aim.2006.05.007
Copyright Status
Unknown
Socpus ID
33750965008 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/33750965008
STARS Citation
Ismail, Mourad E.H. and Zhang, Changgui, "Zeros Of Entire Functions And A Problem Of Ramanujan" (2007). Scopus Export 2000s. 6906.
https://stars.library.ucf.edu/scopus2000/6906