Jacobi elliptic functions
![Elliptic Jacobi function, sn, corresponding to k = 0.8, generated using a version of the domain coloring method.[1]](/uploads/202501/21/Sn-k-080540.png)
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In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance. Many of their features show up in important structures and have direct relevance to some applications (e.g. the equation of a pendulum—also see pendulum (mathematics)). They also have useful analogies to the functions of trigonometry, as indicated by the matching notation sn for sin. The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis to be defined and/or understood. They were introduced by Carl Gustav JakobJacobi (1829).