I was trying to find, where z is complex and n is a constant.
Let z = ln(t), then dz = (1/t)dt. This transforms the integral to
Is this correct? And what would the graph of this look like?
What is C?
C is some simple closed curve about 0.
Why is it holomorphic on C?
Since the partial derivatives are continuous for alland satisfy the CauchyRiemann equations and , is holomorphic on the complex plane.
Thanks for that, I did not know of this method. Is that the only way to show a function like this is holomorphic on C? Would I have to do this before I evaluate any contour integral?
Oh wait, I just noticed...
and sincefor n ≠ 1, z ∈ Z, then every term reduces to zero, so the contour integral is zero... right?