On Computing Jacobi's Elliptic Function sn

2018/03/09 by Ernest Scheiber, Scheiber, Ernest
Computer Science · Mathematics · #33F05 #65D20 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1803.05017

openalex publication_date 2018/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The paper presents a method to compute the Jacobi's elliptic function 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∈ [0,K]∪[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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