2020•Studia Scientiarum Mathematicarum HungaricaOpen access

Lemniscate and exponential starlikeness of regular Coulomb wave functions

İbrahim Aktaş

Abstract

Abstract In this study, a normalized form of regular Coulomb wave function is considered. By using the differential subordinations method due to Miller and Mocanu, we determine some conditions on the parameters such that the normalized regular Coulomb wave function is lemniscate starlike and exponential starlike in the open unit disk, respectively. In additon, by using the relationship between the regular Coulomb wave function and the Bessel function of the first kind we give some conditions for which the classical Bessel function of the first kind is lemniscate and exponential starlike in the unit disk 𝔻.

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Key concepts: Coulomb wave function, Coulomb, Unit disk, Subordination (linguistics), Exponential function, Wave function, Function (biology), Mathematics