2016/05/22 by Árpád Baricz, Baricz, Árpád, Murat Çağlar +5
Mathematics · #30C15 #30C45 #33C10 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1605.06763
openalex publication_date 2016/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper our aim is to determine the radii of univalence, starlikeness and convexity of the normalized regular Coulomb wave functions for two different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for regular Coulomb wave functions, and properties of zeros of the regular Coulomb wave functions and their derivatives. Moreover, by using the technique of differential subordinations we present some conditions on the parameters of the regular Coulomb wave function in order to have a starlike normalized form. In addition, by using the Euler-Rayleigh inequalities we obtain some tight bounds for the radii of starlikeness of the normalized regular Coulomb wave functions. Some open problems for the zeros of the regular Coulomb wave functions are also stated which may be of interest for further research.