Hi!

I'm looking for information about this approximation of a double integral over region [-1,1]x[-1,1]:

$\displaystyle

\int _{-1}^1\int _{-1}^1f(x,y)dxdy

$

$\displaystyle

\approx\frac{5}{9}[f(r,s)+f(r,-s)+f(-r,s)+f(-r,-s)]+\frac{20}{63}[f(0,t)+f(0,-t)]+\frac{8}{7}f(0,0)

$,

where $\displaystyle r=\sqrt{3/5}, s=\sqrt{1/3}, t=\sqrt{14/15}$.

I think it's called Radon's formula for 7 points. I'd like to know more about this approximation, especially how it's derived and if there's more general formula.

If anyone knows anything about it I'd be grateful. I've been trying to google it, but with no success (I don't know if it has different names).

Thank you!