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Jacobi elliptic functions

2020
Jacobi elliptic functions are a realization of one of the simplest cases of elliptic functions, as described in Chapter 14: functions with two simple poles in a period parallelogram that are odd around each pole. These functions come up naturally in certain problems of mechanics, such as the motion of an ideal pendulum.
Richard Beals, Roderick S. C. Wong
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Expression of Elliptic Functions in Terms of Jacobi Functions

Russian Mathematics, 2022
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Jacobi Elliptic Functions

2021
Topic of this chapter are the Jacobi elliptic functions sn, cn, dn, their first derivatives, the additional nine Jacobi elliptic functions, and the amplitude function am. The evaluation of the Jacobi elliptic functions is based on the Jacobi 𝜗 functions and in case of convergency issues additionally on the Gauss hypergeometric function.
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