A short proof of a theorem of Bertilsson by direct use of Löwner’s method
LetS denote the class of schlicht functions. D. Bertilsson proved recently that forf∈S, p<0 and1<-N<-2|p|+1 the modulus of theNth Taylor coefficient of (f′)p takes its maximal value iff is the Koebe function. Here a short proof of a generalisation of this result is presented.