I have a problem with the following integral
$$\int_0^\infty\dfrac{{\rm e}^{-t-(x^2-a^2)/t}}{t}Erf\left(\frac{a}{\sqrt{t}}\right)\,{\rm d}t, $$
where $0\le a<x$ and Erf stands for the error function. I tried to solve that integral using the partial integration; also I found the derivation of such expression with respect to $a$ and then I try to integrate the new expression... but I only get a more complicated version.
Also, I found a document with various integrals of the Error function
http://nvlpubs.nist.gov/nistpubs/jres/73B/jresv73Bn1p1_A1b.pdf
and the similar formula is on page 9 (Equation 32), but it is not the same...
Please if you have some suggestions how to solve such integral?