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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The second coefficient of univalent Bieberbach-Eilenberg functions near the identity


Author: J. A. Hummel
Journal: Proc. Amer. Math. Soc. 80 (1980), 237-243
MSC: Primary 30C50; Secondary 30C70
DOI: https://doi.org/10.1090/S0002-9939-1980-0577751-9
MathSciNet review: 577751
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Abstract: An asymptotic expansion is found for the maximum $ \vert{b_2}\vert$, in terms of $ \beta = 1 - \vert{b_1}\vert$, for functions $ F(z) = {b_1}z + {b_2}{z^2} + \cdots $ which are in the class of univalent Bieberbach-Eilenberg functions and which are near the identity ($ {b_1}$ near 1). The first two terms of this expansion are the same as the expansion of $ \vert{b_2}\vert$ in terms of $ 1 - {b_1}$ for the functions which map the unit disc onto the interior of circles passing through $ \pm 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0577751-9
Article copyright: © Copyright 1980 American Mathematical Society