Jacobi Zeta Function

Let $0\leqslant \phi\leqslant\frac{\pi}{2}$ and $-1 < k < 1$, this calculator evaluates the Jacobi zeta function $Z(\phi,k)$: \[ Z(\phi,k)=E(\phi,k)-\frac{E(k)F(\phi,k)}{K(k)} \] Note that there is no complete counterpart of this function, where $\phi=\pi/2$, as this takes the values zero for all $k$.

Jacobi Zeta Function Calculator