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I know how to calculate residues of several functions, but I really don't know what residue is. Is there any way to really explain what residue is?

AstroFox
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    For one, it's the coefficient from a Laurent series expansion – Ben Grossmann Oct 24 '16 at 00:34
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    See http://math.stackexchange.com/a/255874/589. – lhf Oct 24 '16 at 00:39
  • Could it be the solution to division by zero? After all, it is finding something at the pole(s) of a function. – AstroFox Oct 24 '16 at 00:57
  • AstroFox - the integral is around the pole, not through it. –  Oct 24 '16 at 00:59
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    @AstroFox: In a word, "no". First, division by zero has no meaning in the context of arithmetic. Second, the residue of a simple pole can be an arbitrary complex number, while "the solution to division by zero" would have a single value (if it were to have any arithmetic utility). Third, the functions $f(z) = 1/z^{n}$ ($n \geq 2$ an integer) "involve division by zero" at $z = 0$, but each has residue equal to zero. – Andrew D. Hwang Oct 24 '16 at 01:04
  • I guess that makes sense. It is quite interesting to study the whole phenomena with singularities and discontinuities of functions. Thanks for the quick answers! – AstroFox Oct 24 '16 at 01:45

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