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On the zeros of the second and third Jackson q-Bessel functions and their associated q-Hankel transforms

Published online by Cambridge University Press:  01 July 2009

M. H. ANNABY  and
Z. S. MANSOUR
M. H. ANNABY
Affiliation:
Department of Mathematics & Physics, Qatar University, P.O. Box 2713 Doha, Qatar. e-mail: [email protected], [email protected]
Z. S. MANSOUR
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt. e-mail: [email protected]
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Abstract

We investigate the zeros of q-Bessel functions of the second and third types as well as those of the associated finite q-Hankel transforms. We derive asymptotic relations of the zeros of the q-Bessel functions by comparison with zeros of the theta function. The asymptotics of q-Bessel functions are also given. Zeros of finite q-Hankel transforms of q-summable functions are shown to be real and simple except for a finite number of possible non real zeros. Sufficient conditions are given to guarantee that all zeros are real. We give some applications concerning zeros of combinations of q-Bessel functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 1 , July 2009 , pp. 47 - 67
Copyright
Copyright © Cambridge Philosophical Society 2009

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