Coefficients of odd univalent functions

Hu, Ke

doi:10.1090/S0002-9939-1986-0813835-0

Coefficients of odd univalent functions

Author: Ke Hu
Journal: Proc. Amer. Math. Soc. 96 (1986), 183-186
MSC: Primary 30C50; Secondary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1986-0813835-0
MathSciNet review: 813835
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Abstract: Let

$\displaystyle {S_2} = \left\{ {{f_2}(z) = z + \sum\limits_{n = 1}^\infty {{b_n}{z^{2n + 1}}} \in S} \right\}.$

In this note we prove $\left\vert {{b_n}} \right\vert < 1.1305$ . This is an improvement of V. I. Milin's result [1].

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[5] Kung Sun, Contributions to the theory of schlicht functions. II: The coefficient problem, Sci. Sinica 4 (1955), 359-373.
[6] L. de Branges, A proof of the Bieberbach conjecture, Steklov Mat. Inst., LOMI, preprint E-5-84, Leningrad, 1984, pp. 1-21.