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arXiv · 1802.05226

Geometric and monotonic properties of hyper-Bessel functions

İbrahim Aktaş·Árpád Baricz·Sanjeev Singh
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Abstract

Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some transcendental equations. In addition, we give some bounds for the first positive zero of normalized hyper-Bessel functions, Redheffer-type inequalities, and bounds for this function. In this study we take advantage of Euler-Rayleigh inequalities and Laguerre-Pólya class of real entire functions, intensively.

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İbrahim Aktaş, Árpád Baricz, Sanjeev Singh. 2018-02-14. Geometric and monotonic properties of hyper-Bessel functions. https://doi.org/10.1007/s11139-018-0105-9

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