On some geometric properties of normalized Wright functions

TL;DR

This paper investigates geometric properties like radii of starlikeness and convexity of normalized Wright functions, using their infinite product representations and zero distributions.

Contribution

It determines specific radii of starlikeness and convexity for Wright functions related to lemniscate and Janowski functions, advancing geometric function theory.

Findings

Identified radii of starlikeness for Wright functions.

Established convexity radii for Wright functions.

Utilized infinite product representations and zero properties.

Abstract

The main purpose of the present paper is to determine the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1,$ of normalized Wright functions. The key tools in the proof of our main results are the infinite product representation of Wright function and properties of real zeros of the Wright function and its derivative.