I am trying to convolve two functions:
$f(t) = e^{-h t}$
$g(t) = e^{-(e^{-t})^2}$
$(f*g)(t) = \int_{0}^{t} f(t-\tau)g(\tau) d\tau = \int_{0}^{t} e^{-h(t-\tau)} e^{-(e^{-\tau})^2} d\tau$
Unfortunately, neither Mathematica nor Maple mastered this integral.
Are there any ways to approximate the convolution operator and get at least an approximate solution?
I would be grateful for any advice and help.