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arXiv · 1803.05017

On Computing Jacobi's Elliptic Function \texttt{sn}

Ernest Scheiber
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Abstract

The paper presents a method to compute the Jacobi's elliptic function \texttt{sn} on the period parallelogram. For fixed $m$ it requires first to compute the complete elliptic integrals $K=K(m)$ and $K'=K(1-m).$ The Newton method is used to compute sn(z,m), when $z\in [0,K]\cup[0,i K').$ The computation in any other point does not require the usage of any numerical procedure, it is done only with the help of the properties of sn.

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Ernest Scheiber. 2018-03-09. On Computing Jacobi's Elliptic Function \texttt{sn}. https://arxiv.org/abs/1803.05017

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