The `EllipticK(k)` function returns the complete elliptic integral of the first kind, i.e. the definite integral between 0 and pi/2 of the function `(1-(k*sin(p))**2)**(-0.5)`. The domain of `k` is -1 to 1 (exclusive).
The `EllipticE(k)` function returns the complete elliptic integral of the second kind, i.e. the definite integral between 0 and pi/2 of the function `(1-(k*sin(p))**2)**0.5`. The domain of `k` is -1 to 1 (inclusive).
The `EllipticPi(n,k)` function returns the complete elliptic integral of the third kind, i.e. the definite integral between 0 and pi/2 of the function `(1-(k*sin(p))**2)**(-0.5)/(1-n*sin(p)**2)`. The parameter `n` must be less than 1, while `k` must lie between -1 and 1 (exclusive). Note that by definition EllipticPi(0,k) == EllipticK(k) for all possible values of `k`.