Hi,

I am not a mathematician although I use it in hydrodynamics research. I have a question regarding elliptic integrals for my research in wave theory

Given the value of the complete elliptic integral of the first kind K(k) is there a closed form way to find the elliptic modulus k. If not is there a fast numerical algorithm to evaluate it?

$K(k) = \int_0^{\pi/2} \frac{d\theta}{\sqrt{1-k^2 \sin^2\theta}}$

Thanks