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If $f(x)=\text{arccot}(x)$ for non-negative $x$ and $0$ otherwise, how can I calculate

$$\int_{-\infty}^\infty f(x)f(y-x)\, \mathrm dx$$

for $y\in\mathbb{R}$?

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    The question is when the convolution of two functions exist?2013-06-11

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