Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4622785 | Journal of Mathematical Analysis and Applications | 2006 | 13 Pages |
Abstract
In this article we prove that the basic finite Hankel transform whose kernel is the third-type Jackson q-Bessel function has only infinitely many real and simple zeros, provided that q satisfies a condition additional to the standard one. We also study the asymptotic behavior of the zeros. The obtained results are applied to investigate the zeros of q-Bessel functions as well as the zeros of q-trigonometric functions. A basic analog of a theorem of G. Pólya (1918) on the zeros of sine and cosine transformations is also given.
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