On starlikeness of regular Coulomb wave functions

Baricz, Árpád; Kumar, Pranav; Singh, Sanjeev

doi:10.1090/proc/16180

On starlikeness of regular Coulomb wave functions
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by Árpád Baricz, Pranav Kumar and Sanjeev Singh

Proc. Amer. Math. Soc. 151 (2023), 2325-2338

DOI: https://doi.org/10.1090/proc/16180

Published electronically: March 9, 2023

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Abstract:

In this paper, we study some geometric properties of a class of analytic functions which is defined from the $J$-fraction expansion of the ratio ${zf’(z)}/{f(z)}$. We find the disk domain which is mapped into a starlike domain by these functions. Moreover, we study similar results for two different normalized forms of regular Coulomb wave functions and a normalized Bessel function of the first kind by using continued fractions expansions.

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