Bacle H
Posts:
283
Registered:
4/8/12


existence of holomorphic log in simplyconnected region not containing {0}
Posted:
Oct 11, 2012 7:37 PM


Hi, All:
I'm looking for a proof of the existence of a holomorphic log in
a region R that are simplyconnected but do not wind around the origin.
My idea is:
logz is defined as the integral Int_Gamma dz/z , for Gamma a simpleclosed
curve. The log is then welldefined , since, in simplyconnected regions,
the integral is independent of path. In addition, 1/z is holomorphic
since z=/0 in R . Then the integral is welldefined and holomorphic,
(integral of holomorphic function is holomorphic ) , so the log exists.
Is this O.K?
that

