Close-to-Convexity of Some Special Functions and Their Derivatives

By 'Arp'ad Baricz, R'obert Sz'asz. 2014

53 citations recorded by the source corpus.

In this paper our aim is to deduce some sufficient (and necessary) conditions for the close-to-convexity of some special functions and their derivatives, like Bessel functions, Struve functions, and a particular case of Lommel functions of the first kind, which can be expressed in terms of the hypergeometric function $${}_1F_2$$1F2. The key tool in our proofs is a result of Shah and Trimble about transcendental entire functions with univalent derivatives. Moreover, a known result of Pólya on entire functions, the infinite product representations and some results on zeros of Bessel, Struve, and Lommel functions of the first kind are used in order to achieve the main results of the paper.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aff680620450d060e2c8ea272a051ac66ef90e94

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Bounds for radii of starlikeness and convexity of some special functions (2016, background): “In the sixties Brown, Kreyszig and Todd, Wilf (see [14, 15, 16, 19, 23]) considered the univalence and starlikeness of Bessel functions of the first kind, while in the recent years the radii of univalence, starlikeness and convexity for the normalized forms of Bessel, Struve and Lommel functions of ”
Geometric properties of some Lommel and Struve functions (2014, methodology): “Geometric properties of the Lommel function sμ− 1 2 , 1 2 and of the Struve function Hν were obtained in [3,5] and in [9,15], respectively.”