HI all,

I encountered an integral

$\displaystyle \gamma(x,t)=\pi^{-0.5} \frac{x}{2} \int^t_0 t'^{-\frac{3}{2}} e^{-\frac{x^2}{4t'}} dt' = -\frac{2}{\sqrt{\pi}} \int^t_0 e^{-(\frac{x}{2\sqrt{t'}})^2} d \frac{x}{2\sqrt{t'}} = \frac{2}{\sqrt{\pi}} \int^{\infty}_l e^{-l'^2} d l' = erfc({\frac{x}{2\sqrt{t}}})$

So it's a complementary error function finally.

But it seems that when x=0, the lhs of the equation is equal to 0, while at the rhs, it's equal to 1. So x=0 may not be valid for the error function, since then the integral variable x/2/sqrt(t) is all the time 0. By arguing this, I believe that when x=0, gamma = 0, but then I think that the rhs should be valid for all the finite x, which means that when x is very small but not zero, the rhs and lhs should be the same, which seems not to be the case here.... what went wrong here? Thanks