Coefficient estimates for close-to-convex functions with argument $\beta$

Abstract

This paper deals with coefficient estimates for close-to-convex functions with argument $\beta$ ($-\pi/2<\beta<\pi/2$). By using Herglotz representation formula, sharp bounds of coefficients are obtained. In particluar, we solve the problem posed by A. W. Goodman and E. B. Saff in $\cite{GS}$. Finally some complicted computations yield the explicit estimate of the third coefficient.