How can I integrate the degenerate multidimensional Gaussian?

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Saso Tomazic

se attached for two dimensions. It straigth forward to generalize.

Sorry, my mistake, Iowerlooked ()^2

Pengda Huang

Thank you, Dr. Tomazic. :)

Correct solution is somehow more difficult. See the attachement.

Dr. Tomazic,

Thank you so much! Could you please teach me more about the background knowledge to solve this integral? 'Dawson Integral' is the only key point to calculate this integral? Thanks,

Regards,

Pengda

When you integrate Gaussian function you end up with erf, so you cannot avoid Dawson Integral or some other integral that include erf.

To come to the solution I cheated. I used Wolfram Mathematica. I always do when I come acros an integral or differential equation difficult to solve.

So there is solution with erf instead of Dowson integral