Coefficient estimates for close-to-convex functions with argument $β$

This paper deals with coefficient estimates for close-to-convex functions with argument $β$ ($-π/2<β<π/2$). 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.

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