On the Janowski Starlikeness of the Coulomb Wave Functions

Abstract

In this article, we are interested in finding sufficient conditions on $A,B,L$ , and $\eta$ which ensure the normalized Coulomb wave function to be Janowski starlike. Sufficient conditions are also obtained for $g_{L,\eta }/z\in \mathcal{P}\left[A,B\right]$ , which readily yield conditions for $g_{L,\eta }$ to be close-to-convex.