On the logarithmic coefficients of close to convex functions (Q2790274)

For a normalized analytic function \(f\), define the logarithmic coefficients \(\gamma_n\) by NEWLINENEWLINE\[NEWLINE\log\frac{f(z)}{z} = 2\sum_{n=1}^{\infty}\gamma_nz^n.NEWLINE\]NEWLINE Let \(f\) be analytic and close to convex in the unit disk \(\mathbb D\). This means that there exists a star-like function \(g\) such that NEWLINE\[NEWLINE\mathrm{Re} \frac{zf'(z)}{g(z)} > 0, \quad z \in \mathbb D.NEWLINE\]NEWLINE The author obtains sharp estimates for the logarithmic coefficients \(\gamma_1, \gamma_2, \gamma_3\) of close to convex functions.