Bounds for Radii of Starlikeness of Some $${\varvec{q}}$$ q -Bessel Functions

Bounds for Radii of Starlikeness of Some $${\varvec{q}}$$ q -Bessel Functions In this paper the radii of starlikeness of Jackson’s second and third q-Bessel functions are considered and for each of them three different normalization are applied. By applying Euler–Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre–Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

Bounds for Radii of Starlikeness of Some $${\varvec{q}}$$ q -Bessel Functions

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-017-0668-6
Publisher site
See Article on Publisher Site

Abstract

In this paper the radii of starlikeness of Jackson’s second and third q-Bessel functions are considered and for each of them three different normalization are applied. By applying Euler–Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre–Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Journal

Results in MathematicsSpringer Journals

Published: Mar 21, 2017

References

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