The statement concerns the Taylor coefficients an of a univalent function, i.e. a one-to-one holomorphic function that maps the unit disk into the complex plane, normalized as is always possible so that a0 = 0 and a1 = 1. That is, we consider a function defined on the open unit disk which is holomorphic and injective (univalent) with Taylor series of the form
Such functions are called schlicht. The theorem then states that
The Koebe function (see below) is a function in which an = n for all n, and it is schlicht, so we cannot find a stricter limit on the absolute value of the nth coefficient.