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Math Help - Simple complex analysis question

  1. #1
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    Simple complex analysis question

    Winding direction: With residues, is there some trick to picking the winding direction or do I just get to pick what I want? I'm specifically looking at the solution to the Klein-Gordon equation. It appears that all the sources are just picking the winding direction that is handy. For this specific problem, that's fine because it has a multitude of eigenvalues.

    However, in general, is there any trick to picking a winding direction OR do contour integrals always have multiple answers?

    Thanks!
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  2. #2
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    Pick it however you want. But- if you are going clockwise, the integral will be the negative of the sum of the residues. That's because the "convention" is to integrate around a closed path counterclockwise and switching directions multiplies the integral by -1.
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