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Zeros of entire functions and a problem of Ramanujan |
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| Authors: | Mourad EH Ismail Changgui Zhang |
| Institution: | a Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA b Laboratoire Paul Painlevé UFR Math., Université des Sciences et Technologie de Lille, Cité Scientifique, 59655 Villeneuve d'Ascq cedex, France |
| 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. |
| Keywords: | primary 33D45 secondary 33E05 |
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