- #1
agalliasthe
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Homework Statement
This is a question I'm trying to solve for chemistry research - but is homework-like, so I thought it best fit in this category.
Homework Equations
I am trying to find the indefinite integral of:
[tex]F(x,y)=\int \int e^{-k_1x^2-k_2y^2+k_3xy} dx dy [/tex]
[tex] k_1, k_2, k_3 [/tex] are constants
The Attempt at a Solution
I realize that the solution involves the error function. When I reduce it to:
[tex]F(x,y)=\int e^{-k_2 y^2} dy \int e^{-k_1x^2+k_3xy} dx [/tex]
I am not sure how to treat the terms in the dx integral.
When I ask WolphramAlpha, it tells me:
[tex] \int e^{-k_1 x^2+k_3xy} = \frac{\sqrt{\pi}exp(\frac{k_3^2y^2}{4k_1})}{2 \sqrt {k_1}}erf\left( \frac{2k_1x-k_3y}{2\sqrt{k_1}}\right )+c [/tex]
but I'm not sure how they got this and I'm not sure how to proceed from here. I haven't been able to find a good erf integral table. Can you offer a suggestion on a way to solve this?Thanks.