Coefficients of meromorphic schlicht functions

Duren, Peter L.

doi:10.1090/S0002-9939-1971-0271329-7

Coefficients of meromorphic schlicht functions
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Proc. Amer. Math. Soc. 28 (1971), 169-172 Request permission

Abstract:

This paper presents an elementary proof of a known theorem on the coefficients of meromorphic schlicht functions: if $f \in \Sigma$ and ${b_k} = 0$ for $1 \leqq k < n/2$, then $|{b_n}| \leqq 2/(n + 1)$.

References

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P. R. Garabedian and M. Schiffer, A coefficient inequality for schlicht functions, Ann. of Math. (2) 61 (1955), 116–136. MR 66457, DOI 10.2307/1969623

Some estimates of the coefficients of schlicht functions

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On $p$-valent functions

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