Complete elliptic integral of the first kind
= Complete elliptic integral of the first kind
{title2=$K(k)$}
For $0<k<1$, the complete elliptic integral of the first kind is
$$
K(k)=\int_0^1\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}.
$$
It is the complete first-kind member of the <elliptic integral> family.