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Complex analysis - partial fraction expansion
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[QUOTE="brmath, post: 4543142, member: 486151"] I've been trying myself to sort out this Laurent series stuff, but I'm pretty sure I'm not following this. Would you mind answering some questions? Are we trying to find a function g(z) to expand in a Laurent series which will match the summation at z = n? I understand that any appropriate g would have simple poles at ±ai, so would have just the ##a_{-1}## term in its Laurent series. But why would this residue necessarily show up in the other terms of the Laurent series? Does this Laurent series converge to g everywhere? Somehow I'm thinking that the series around ai is good only down to -ai -- that is converges in a radius of 2a around the point +ai. Or am I completely on the wrong track here? If you can explain, I would very much appreciate it. [/QUOTE]
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Complex analysis - partial fraction expansion
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