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If I have $\sum_{n=1}^{\infty}f(x)g(x)$, is there any way to split this up? Thanks.

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will this help ?? en.wikipedia.org/wiki/Summation_by_parts#Method –  r9m Mar 5 '14 at 6:07
cauchy product for one –  James S. Cook Mar 5 '14 at 6:12
The product as given is an infinite summation over the constant $f(x)g(x)$. If it were $f(n)g(n)$ or $f(n+x)g(n+x)$ there are Fourier series and the Parseval identity to consider. –  LutzL Mar 7 '14 at 18:46

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