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It's been ages since I took complex analysis, but I distinctly remember the first time I used contour integration to solve a convoluted definite integral and be
by ohazi 10y ago
It's been ages since I took complex analysis, but I distinctly remember the first time I used contour integration to solve a convoluted definite integral and being absolutely floored that I got the right answer. The technique looks like super hand-wavey bullshit, and the algebra usually ends up being way easier than you think is reasonable for a given problem.
I'm still amazed that it works.
Example: https://en.wikipedia.org/wiki/Residue_theorem https://en.wikipedia.org/wiki/Residue_theorem
- chestervonwinch 10y agoFor the integral in the post, it's not so straight-forward to use complex contour integration [1]. Though, I agree with you -- for many other similarly intimidating integrals, complex integration can work wonders. [1]: http://www.jstor.org/stable/2588989?seq=1#page_scan_tab_contents http://www.jstor.org/stable/2588989?seq=1#page_scan_tab_cont...
- vardhanw 10y agoI recently came across a beautiful application of it to solve one of Ramanujan's integrals [1]. [1] http://math.stackexchange.com/questions/808452/proof-of-a-ramanujan-integral http://math.stackexchange.com/questions/808452/proof-of-a-ra...