Does somebody know if there's somewhat an analytical solution to the Gaussian integral on a semi-plan:
$\frac{1}{\sqrt{2\pi}}\int_{x<c}e^{-\frac{(x^2+y^2)}{2}}dxdy$
Thanks!
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Is it the integral $\frac{1}{\sqrt{2\pi}} \int_{-\infty}^c \int_{-\infty}^c e^{-\frac{x^2+y^2}{2}} dxdy$ you want to find an analytical solution to? – Wisław Oct 10 '17 at 21:15
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No, $y$ goes from $-\infty$ to $+\infty$, but actually I think my question if pretty dumb as the integral is separable... – Vincz777 Oct 10 '17 at 21:17
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Yes exactly, and then your integral is simply equal to $\int_{-\infty}^c e^{-\frac{x^2}2} dx$, which can not be written in terms of elementary functions. – Wisław Oct 10 '17 at 21:20
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Thanks, but I can use the $erf$ function, right? Which is available in numerical packages. – Vincz777 Oct 10 '17 at 21:21