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    $\begingroup$ You mean aside from the bajillion problems you can solve by analytic extension and the method of residuals? $\endgroup$ Commented Feb 24, 2014 at 1:36
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    $\begingroup$ @dmckee: I actually don't know about the bajillion problems you mention. I know about the method of residues, but is it really that important? It's obviously pretty neat, but I didn't imagine it would be so useful. Maybe you should mention all of this in an answer. $\endgroup$ Commented Feb 24, 2014 at 1:38
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    $\begingroup$ Just found this very closely related question: physics.stackexchange.com/q/89072 $\endgroup$ Commented Feb 24, 2014 at 2:35
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    $\begingroup$ @ChrisWhite also this physics.stackexchange.com/q/45981 $\endgroup$ Commented Feb 24, 2014 at 2:56
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    $\begingroup$ @nervxxx: I'm not saying it isn't applicable, I'm just saying that I haven't seen any applications. That's why I'm asking this question instead of going to the math department to complain about being taught useless stuff. $\endgroup$ Commented Feb 24, 2014 at 2:58