The th Coefficient in the Power series of a Univalent Function should be no greater than . In
other words, if
References
de Branges, L. ``A Proof of the Bieberbach Conjecture.'' Acta Math. 154, 137-152, 1985.
Hayman, W. K. Multivalent Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1994.
Hayman, W. K. and Stewart, F. M. ``Real Inequalities with Applications to Function Theory.'' Proc. Cambridge Phil. Soc. 50,
250-260, 1954.
Kazarinoff, N. D. ``Special Functions and the Bieberbach Conjecture.'' Amer. Math. Monthly 95, 689-696, 1988.
Korevaar, J. ``Ludwig Bieberbach's Conjecture and its Proof.'' Amer. Math. Monthly 93, 505-513, 1986.
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 53, 1983.
Pederson, R. N. ``A Proof of the Bieberbach Conjecture for the Sixth Coefficient.'' Arch. Rational Mech. Anal. 31,
331-351, 1968/1969.
Pederson, R. and Schiffer, M. ``A Proof of the Bieberbach Conjecture for the Fifth Coefficient.'' Arch. Rational Mech. Anal.
45, 161-193, 1972.
Stewart, I. ``The Bieberbach Conjecture.'' In From Here to Infinity: A Guide to Today's Mathematics.
Oxford, England: Oxford University Press, pp. 164-166, 1996.