Contrôle Continu Analyse Complexe L3 - UCA

fD C
n∈N∗f0(1
2−1 n)=0 f(1 2) = 2 f(0)
Log f(z) = 1
2iLog 1 + iz 1−iz 
z∈C\ {−i}Z=1 + iz
1−iz Z
Z∈R−z=ib b ∈]− ∞,−1] ∪[1,+∞[
U f R⊂U
U
ζ∈C\π
2+πZtan ζ=ei2ζ−1
i(ei2ζ+ 1)
z∈U f(z)∈C\π
2+πZtan(f(z))
f0U