How do you integrate f(z) = e^(1/z) in the multiply connected domain {Rez>0}∖{2}
It seems like integrals of this function are path independent in this domain since integrals of e^(1/z) exist everywhere in teh domain {Rez>0}∖{2}. Is that correct?
Are the integrals of the function f(z) = (1/(z-2) + (1/(z+1) + e^(1/z)
path independent in the following domain: {Rez>0}∖{2}
The domain is not simply connected
I know that path independence has 3 equivalent forms
that are
1) Integrals are independent if for every 2 points and 2 contours...
Assume |f(z)| >= 1/3|e^(z^2)| for all z in C and that f(0) = 1 and that f(z) is entire. Prove that f(z) = e^(z^2) for all z in C.
How do you start for this.