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Proceedings of the American Mathematical Society

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

 
 

 

Coefficients for the area theorem


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 33 (1972), 438-444
MSC: Primary 30A34
DOI: https://doi.org/10.1090/S0002-9939-1972-0291437-5
MathSciNet review: 0291437
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Abstract: Let $f(z) = \sum \nolimits _{n = 1}^\infty {{a_n}{z^n}}$, and set $G(z) = f{({z^{ - p}})^{ - /1p}} = \sum \nolimits _{n = 0}^\infty {{g_{np - 1}}{z^{1 - np}}}$. This paper finds an explicit formula for ${g_{np - 1}}$ in terms of the ${a_n}$. Such a formula (apparently previously unknown) may be very useful in the theory of univalent functions.


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Keywords: Univalent functions, area theorem, coefficient bounds
Article copyright: © Copyright 1972 American Mathematical Society