If a function f(x) have SIMPLE POLES , could in principle this f(x) be expanded into(adsbygoogle = window.adsbygoogle || []).push({});

[tex] f(x)= \sum_{r}a_{r} (x-r)^{-1} [/tex]

where 'r' are the poles on the complex plane of the function

Another question, would it be possible to relate using the Euler-Mac Laurin resummation, a series of the form [tex] \sum_{n=0}^{\infty}(-1)^{n}f(n) [/tex] to the integral

[tex] \int_{0}^{\infty}f(x)dx [/tex]

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# Expansion of a function f(x) with poles

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