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You are not logged in. #1 20121025 20:52:56
Is this contour integration correct?I was trying to find 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? #2 20121025 22:50:28
Re: Is this contour integration correct?What is C? #3 20121025 22:58:05
Re: Is this contour integration correct?C is some simple closed curve about 0. #4 20121025 23:04:59
Re: Is this contour integration correct?
Then shouldn't it be 0 by Cauchy's integral theorem since is holomorphic on ?
#6 20121026 02:42:19
Re: Is this contour integration correct?
Let so where and .
Since the partial derivatives are continuous for all and satisfy the Cauchy–Riemann equations and , is holomorphic on the complex plane. #7 20121026 03:03:37
Re: Is this contour integration correct?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? #8 20121026 03:10:09
Re: Is this contour integration correct?Oh wait, I just noticed... and since for n ≠ 1, z ∈ Z, then every term reduces to zero, so the contour integral is zero... right? 