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On the Logarithmic Coefficients of Close to Convex Functions

Complex Variables 2015-10-01 v1

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 γn\gamma_{n} of ff defined by logf(z)z=2n=1γnzn\log \dfrac{f(z)}{z}=2\sum_{n=1}^{\infty} \gamma_{n}z^{n} when n=1,2,3n=1, 2,3.

Keywords

Cite

@article{arxiv.1509.08911,
  title  = {On the Logarithmic Coefficients of Close to Convex Functions},
  author = {D. K. Thomas},
  journal= {arXiv preprint arXiv:1509.08911},
  year   = {2015}
}

Comments

Proceedings American Mathematical Society September 2015