For simplicity, what is the explicit expression of integral (3 dimension for example),
\int_{x1} \int_{x2} \int{x3} exp(-(k1*x1+k2*x2+k3*x3)^2) dx1 dx2 dx3
The attached figure shows the integral also.
Happy new year!
Thanks,
se attached for two dimensions. It straigth forward to generalize.
Sorry, my mistake, Iowerlooked ()^2
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
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