On the Logarithmic Coefficients of Close to Convex Functions

preprint2015arXivOpen access

Abstract

For ff analytic and close to convex in D={z:∣z∣<1}D=\{z: |z|< 1\}, we give sharp estimates for the logarithmic coefficients γnγ_{n} of ff defined by log⁡f(z)z=2∑n=1∞γnzn\log \dfrac{f(z)}{z}=2\sum_{n=1}^{\infty} γ_{n}z^{n} when n=1,2,3n=1, 2,3.

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