CommandsEllipticKOn this pageEllipticK EllipticK (x) The EllipticK function returns the complete elliptic integral of the first kind, K(k)=∫01dt(1−t2)(1−k2t2),\displaystyle K(k)=\int_{0}^{1} \frac{d t}{\sqrt{\left(1-t^{2}\right)\left(1-k^{2} t^{2}\right)}},K(k)=∫01(1−t2)(1−k2t2)dt, with 0≤k≤1.\displaystyle 0 \leq k \leq 1 .0≤k≤1. See Also EllipticE, GeometricMean