What is the cross-correlation function of two gaussians

Hi everyone,

Earlier I posted a question regarding the probability of one gaussian distribution being similar to another one.

I might have stumbled on something that might answer the question but I'm not sure. I found out that the expectation of the __difference__ of two gaussians can be calculated from their __cross-correlation integral__.

From Wolfram's Mathworld pages I found the __convolution integral__ of two gaussians (which is the expectation of __sum__ of two gaussians) but they didn't give explicit form of the cross-correlation of two gaussian functions.

Would this be the right way to calculate how similar two gaussians are?

If yes, does anyone know how to derive the cross-correlation of gaussians, or have the final answer at hand.

Your help is much appreciated.

Cheers,