Radii of starlikeness of some special functions

TL;DR

This paper investigates the geometric property of starlikeness for certain normalized Lommel and Struve functions, precisely determining their radii of starlikeness within the unit disk.

Contribution

It provides exact calculations of the radii of starlikeness for six normalized special functions, expanding understanding of their geometric behavior.

Findings

Exact radii of starlikeness for six functions determined.

Normalizations ensure functions are analytic in the unit disk.

Results contribute to geometric function theory.

Abstract

Geometric properties of the classical Lommel and Struve functions, both of the first kind, are studied. For each of them, there different normalizations are applied in such a way that the resulting functions are analytic in the unit disc of the complex plane. For each of the six functions we determine the radius of starlikeness precisely.