Is there a closed form formula for the convolution of $1/(1+x^2)$ and $\exp(-x^2/(4t))$, where $t>0$, i.e. the integral
$$\int\_{-\infty}^\infty \frac{1}{1+u^2}\exp\left(-\frac{(x-u)^2}{4t}\right)\,du?$$
I doubt it, but someone may be able to use special functions.