On the zeros of basic finite Hankel transforms |
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Authors: | MH Annaby ZS Mansour |
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Institution: | Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt |
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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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Keywords: | Basic hypergeometric series Zeros of q-functions Zeros of entire functions of order zero |
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