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>the series expansion of 1/(1+x^2) around 1 has a radius of convergence √2 because this is the distance from between 1 and the function's nearest singularity (which is at i) when you view x as an element of the complex plane
Why is complex analysis so beautiful, anons?
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>>8971176
Such is the nature of "imaginary" worlds.
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>if two functions are holomorphic on a connected open set D and the functions are equal on a subset of D that has a limit point inside D, then the functions are equal on the entirety of D
>if f(1/n)=g(1/n) for all n then f=g everywhere
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>the value of a holomorphic function a point is completely determined by the averaging the function's values around a random loop enclosing that point
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>>8971650
WHoah what the fuck where can I read about this. Got Alfohrs, Bak, and Visual CA on deck, where should I see this magic?
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>>8971653
I sense irony in your post but whatever... (see also page 102 "Averaging over Circles").
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