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 $y\in\mathbb{R}$?
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 $y\in\mathbb{R}$?
$f\left(x\right)$ is this plot but with $f$ zero for $x < 0$ and $f\left(y-x\right)$ is $f\left(x\right)$ flipped about $x = 0$ and then displaced in the positive $x$ direction by $y$. So, for: