jacobi4

]> jacobi4

\begin{array}{rcl} s n (u, k) & \approx & \sin (u) - \frac{1}{4} k^{2} (u - \sin (u) \cos (u)) \cos (u) \\ c n (u, k) & \approx & \cos (u) + \frac{1}{4} k^{2} (u - \sin (u) \cos (u)) \sin (u) \\ d n (u, k) & \approx & 1 - \frac{1}{2} k^{2} \sin^{2} (u) \end{array}