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8 [section:jacobi Jacobi Elliptic Functions]
10 [section:jac_over Overview of the Jacobi Elliptic Functions]
12 There are twelve Jacobi Elliptic functions, of which the three copolar functions ['sn], ['cn] and […
14 …ote [@http://en.wikipedia.org/wiki/Jacobi_elliptic_functions Wikipedia: Jacobi elliptic functions]]
15 …am.com/JacobiEllipticFunctions.html Weisstein, Eric W. "Jacobi Elliptic Functions." From MathWorld…
16 …@http://dlmf.nist.gov/22 Digital Library of Mathematical Functions: Jacobian Elliptic Functions, R…
18 These functions each take two arguments: a parameter, and a variable as described below.
20 Like all elliptic functions these can be parameterised in a number of ways:
26 In our implementation, these functions all take the elliptic modulus /k/ as the parameter.
30 Finally note that our functions all take the elliptic modulus /k/ as the *first* argument - this is…
36 There are twelve functions for computing the twelve individual Jacobi elliptic functions: __jacobi_…
43 Note however that these individual functions are all really thin wrappers around the function __jac…
44 the three copolar functions ['sn], ['cn] and ['dn] in a single function call. 
46 [tip If you need more than one of these functions
49 [endsect] [/section:jac_over Overview of the Jacobi Elliptic Functions]
71 The function __jacobi_elliptic calculates the three copolar Jacobi elliptic functions
76 The functions are defined as follows, given:
89 [caution Rather like other elliptic functions, the Jacobi functions
113 to the functions: this is for alignment with the elliptic integrals which match the requirements
116 be extra careful when using these functions!]
120 The following graphs illustrate how these functions change as /k/ changes: for small /k/
121 these are sine waves, while as /k/ tends to 1 they become hyperbolic functions:
131 These functions are computed using only basic arithmetic operations and trigonometric functions, so
134 functions, grow as the angle increases.
148 calculator at [@http://functions.wolfram.com/ functions.wolfram.com],
556 [endsect] [/section:jacobi Jacobi Elliptic Functions]