# Complex Error Functions as Solutions to Gaussian Integrals

## Main Question or Discussion Point

I have been told that the following integral can be expressed analytically as a combination of error functions of t. And that the solution can be obtained from then by numerically integrating over t.

$$\int^a_b sin(k_1x)sin(k_2x')\int_0^\infty \frac{1}{\sqrt{t}}e^{-t(x-x')^2}dtdx dx'$$

While I don't have a problem with numerical integration, I can't see how the expression becomes a combination of error functions. The root t under the line is giving me trouble as well, as it makes the integral look divergent.

Thanks

-Strictly speaking, this is not course work, as the integral has come up in research. But if that forum is still more appropriate I can move it there.