# Fast computation of complete elliptic integrals and Jacobian elliptic functions

@article{Fukushima2009FastCO, title={Fast computation of complete elliptic integrals and Jacobian elliptic functions}, author={Toshio Fukushima}, journal={Celestial Mechanics and Dynamical Astronomy}, year={2009}, volume={105}, pages={305-328} }

As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9–19 obtained by truncating Taylor series expansions of the integrals. Otherwise, the associate integrals, K(1 − m) and E(1 − m), are first computed…

## 39 Citations

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