Hello, I have problems to show that

$\displaystyle \int_0^{\infty} e^{-ct}\sqrt{\frac{1}{2\pi t}}e^{-(x-y)^2\frac{1}{2t}} dt=\frac{1}{\sqrt{2c}}e^{-\sqrt{2c}|x-y|}$

If one omits the constants then essentially on has to calculate

$\displaystyle \int_0^{\infty}\sqrt{\frac{1}{t}}e^{-t-\frac{1}{t}} dt$.

I can't see, if and how substitution or partial integration could help.

Maybe the residual theorem could help? But I dont see directly how...

Do you have an idea how to calculate this integral? I would be glad, if somebody has.

best regards,

slabic