On Lemniscate starlikeness of analytic functions and its application to special functions

TL;DR

This paper explores conditions under which certain analytic functions are lemniscate starlike, applying these results to special functions and refining existing mathematical understanding of their geometric properties.

Contribution

It introduces new coefficient conditions for lemniscate starlikeness and applies these to various special functions, extending prior research in geometric function theory.

Findings

Derived specific coefficient conditions for lemniscate starlikeness.

Applied conditions to special functions to determine parameter ranges.

Extended and refined earlier results in the domain.

Abstract

This paper investigates the lemniscate starlikeness of analytic functions by deriving specific conditions on their power series coefficients. The study utilizes the Cauchy product of power series along with key inequalities involving the Pochhammer symbol and the Gamma function. The derived results are further applied to a number of special functions, providing parameter restrictions under which these functions become lemniscate starlike. The findings extend and refine several earlier results in this domain.