On Computing Jacobi's Elliptic Function \texttt{sn}
arXiv:1803.050171.2h-index: 4
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This is an incremental improvement for numerical computation of a specific special function.
The paper presents a method to compute Jacobi's elliptic function sn on the period parallelogram using Newton's method for specific intervals and properties elsewhere, without providing concrete performance numbers.
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.