If you are trying to find the integral of a function with a complex pole on the real axis (i.e. ##[-\infty,\infty]##) via analytic continuation, does it matter if you integrate along a contour either in the upper-half plane or lower-half plane? I was under the assumption that either approach was equivalent. For example, if you have a pole at ## a + ib##, where ##a## and ##b## are positive constants, and take your contour to be a semicircle with radius out to infinity, so that by Jordan's lemma that component of the integral goes to 0, then shouldn't either approach (i.e. top half or bottom half of a circle) give you the same answer? It seems that I am missing or incorrectly assuming something obvious here.(adsbygoogle = window.adsbygoogle || []).push({});

(I've attached an image that attempts to depict what I tried to explain above.)

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# I Integration above or below axis

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