Uni Stuff > Mathematics

Complex Analysis

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/0:
Ooohhhh, I see now, thanks =D

/0:
Suppose you need to integrate a real function such as so you introduce a complex function which has poles at the blue crosses in the picture (and some others in the lower half plane that aren't important). Aren't both of the possible contours just as valid as each other? The only difference is that one of them encloses 4 poles while the other only encloses 2, but once you shrink the small semi-cirlces to zero radius they should have zero contribution anyway..

humph:
Of course. But in either case the little semicircles may have a non-neglible contribution even as you shrink them smaller and smaller.

/0:
Ah thanks humph, I skimmed over that lemma before

/0:
Bit of a dumb question here,

If , then why doesn't have a branch cut on the negative real axis (assuming the principal logarithm)?

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