Bieberbach conjecture

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Bieberbach conjecture

[′bē·bə‚bäk kən‚jek·chər]
(mathematics)
The proposition, proven in 1984, that if a function ƒ(z) is analytic and univalent in the unit disk, and if it has the power series expansion z + a2 z 2+ a3 z 3+ ⋯, then, for all n (n = 2, 3, …), the absolute value of an is equal to or less than n.