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DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

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Rewriting an asymptotic series as a convergent integral [closed]

I am given the function $$ f(x) = \sum_{n=1}^{\infty} \frac{\Gamma(2n)}{\Gamma(n)}(-x)^n $$ and I need to show that it can be rewritten as an integral that is convergent for a range of values of x. I …
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