Can you help with this integration
int (inf,-inf)int (z,-inf)( exp-m(square)/2)dm(2Π) exp(-kz) ( exp-z(square)/2)dz
In LaTeX:
$\displaystyle \int^{\infty}_{-\infty} \left( \int^z_{-\infty} e^{-m^2/2}\ dm \right) (2 \pi) e^{-kz} e^{-z^2/2}\ dz$
Which is almost certainly non-elementary, as the integral in the brackets is a error function, or $\displaystyle \sqrt{2 \pi}\Phi(x)$, where $\displaystyle \Phi(x)$ is the cumulative standard normal distribution.
So the question is why do you want this and would a numerical value do?
RonL
This is the original problem
$\displaystyle
\int_{\epsilon+\alpha/k}^{\infty} xF(x)f(x)dx
$
where F(x)=$\displaystyle \Phi(y)$
f(x)=$\displaystyle (2\Pi )^{-1/2} e^{-ky}e^{-y^2/2}$
y=$\displaystyle -k ^{-1}log [1-k(x-\epsilon)/\alpha]$
$\displaystyle \Phi(y)=\int_{-\infty}^{y} e^{-m^2/2} dm$