Coefficients for the area theorem

Goodman, A. W.

doi:10.1090/S0002-9939-1972-0291437-5

Coefficients for the area theorem
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Proc. Amer. Math. Soc. 33 (1972), 438-444 Request permission

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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Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln

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