Radii of convexity of some Lommel and Struve functions

TL;DR

This paper determines the radii of convexity for certain Lommel and Struve functions of the first kind, using three different normalizations, and explores zeros of their derivatives, contributing to complex analysis and special functions.

Contribution

It introduces new results on the convexity radii of Lommel and Struve functions with multiple normalizations and analyzes zeros of their derivatives.

Findings

Radii of convexity for Lommel and Struve functions are explicitly determined.

Three different normalizations ensure analyticity in the unit disk.

Results on zeros of derivatives provide additional insights.

Abstract

The radii of convexity of some Lommel and Struve functions of the first kind are determined. For both of Lommel and Struve functions three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. Some results on the zeros of the derivatives of some Lommel and Struve functions of the first kind are also deduced, which may be of independent interest.