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Mathematics > Classical Analysis and ODEs

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

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.
Comments: 12 pages, 3 figures
Subjects: Classical Analysis and ODEs (math.CA); Numerical Analysis (math.NA)
MSC classes: 65D20, 33F05
Cite as: arXiv:1803.05017 [math.CA]
  (or arXiv:1803.05017v1 [math.CA] for this version)

Submission history

From: Ernest Scheiber [view email]
[v1] Fri, 9 Mar 2018 09:57:13 GMT (69kb,D)