Heuman Lambda Function
Let $0\leqslant \phi\leqslant\frac{\pi}{2}$ and $-1 < k < 1$, this calculator evaluates the Heuman Lambda function $\Lambda_0(\phi,k)$: \[ \Lambda_0(\phi,k)= \frac{F\left(\phi,\sqrt{1-k^2}\right)}{K\left(\sqrt{1-k^2}\right)}+\frac{2}{\pi}K(k) Z\left(\phi,\sqrt{1-k^2}\right) \] Note that there is no complete counterpart of this function, where $\phi=\pi/2$, as this takes the values 1 for all $k$.