On Bieberbach-Eilenberg Functions. III
James A. Jenkins · Transactions of the American Mathematical Society · 1965
V ff » CO \ 2 m 2 a, 2 Amlz))+ 2 pk(Y Am,C,-' oo n/oo \N/oo \ + 2 / 2 a, 2 x"azjn)+ 2 aJI «*"m i = l j = l \m = l / fc=l \m = l / g -2 a^logíl.-z,z» -2 ptprlog(l-£,/£,/).JJ'-l N 2 fc.fc' =1 Let r,p,0 p, let £r be the image of | z | p under F with boundary Ap, each boundary being given the counterclockwise sense.Let Wj=fizf), j = 1, ■•-,n,cok = F{Çk), k = l,---,N.The complement Drp of £r UGp has positive area in the metric 2 tXjiw-Wj) 1+ 2 Ptiw-fflfc) 1 \dw\.where d.4w denotes the element of Euclidean area in the w-plane.We transform this into ¿f-J + J J (? ä/log(w-wy))" +^2 pt(log(w -cu,))-j ■idl 2 a,log(w -Wj) + 2 ptlog(w -cok)\> 0, V? = i * = i / and moreover into --4 Í ft ä, (log(/(z)-/(z,)))-4-2 p,(log(/(z) -TO)")•d(t a,log(/(z)-/(z,))+ 2 p*log(/(z)-Fo)V/ -1 k = 1 / 1 f (2ä/log(F(0-/(z,.)))-+ 2 p^logiFiO-FiQ))-)• d( 2 aylog(F(C) -fizj)) + 2 ptlog(F(0 -FiCk))) > 0.Now we have on | z | = r the Laurent expansion(2)