Jacobi elliptic functions

Elliptic Jacobi function, sn, corresponding to k = 0.8, generated using a version of the domain coloring method.[1]

Model of amplitude (measured along vertical axis) as a function of independent variables u and k

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).

单词	Jacobian function
释义	Jacobian function 英语百科 Jacobi elliptic functions 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).
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Jacobian function

Jacobi elliptic functions