Λ_0(ϕ| m) congruent (F(ϕ|1 - m))/(K(1 - m)) + 2/π K(m) Z(ϕ|1 - m), where ϕ is the Jacobi amplitude, m is the parameter, Z is the Jacobi zeta function, and F(ϕ| m') and K(m) are incomplete and complete elliptic integrals of the first kind.

elliptic integral of the first kind | Jacobi zeta function