On reality and asymptotics of zeros of q-Hankel transforms

M. H. Annaby; Z. S. Mansour; O. A. Ashour

doi:10.1016/j.jat.2008.11.001

On reality and asymptotics of zeros of q-Hankel transforms

M. H. Annaby
, Z. S. Mansour
, O. A. Ashour

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q ∈ (0, 1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.

Original language	English
Pages (from-to)	223-242
Number of pages	20
Journal	Journal of Approximation Theory
Volume	160
Issue number	1-2
DOIs	https://doi.org/10.1016/j.jat.2008.11.001
State	Published - Sep 2009
Externally published	Yes

Keywords

Asymptotics of zeros of q-functions
Zeros of entire functions of order zero
q-Bessel functions

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10.1016/j.jat.2008.11.001

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abstract = "We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouch{\'e}'s theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q ∈ (0, 1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.",

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AU - Annaby, M. H.

AU - Mansour, Z. S.

AU - Ashour, O. A.

PY - 2009/9

Y1 - 2009/9

N2 - We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q ∈ (0, 1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.

AB - We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q ∈ (0, 1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.

KW - Asymptotics of zeros of q-functions

KW - Zeros of entire functions of order zero

KW - q-Bessel functions

UR - https://www.scopus.com/pages/publications/70349839189

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DO - 10.1016/j.jat.2008.11.001

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EP - 242

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 1-2

ER -

On reality and asymptotics of zeros of q-Hankel transforms

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Keywords

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