Maths Elliptic Functions

Calculate maths elliptic functions (sn, cn, and dn). The ellipse is of the form.

`x^2 + (y/b)^2 = 1 `
`m = √(1 - 1/b^2) `
`x = (cn(u, m)) / (dn(u, m)) `
`y = (sn(u, m)) / (dn(u, m)) `

where :

b = the semi major axis (y axis)
u = the elliptic arc length
m = the elliptic parameter

The semi minor axis (x axis) a = 1, and the semi major axis (y axis) b ≥ 1. The elliptic parameter 0 ≤ m ≤ 1. There is an alternative form for m which is used in some methods.

`m' = 1 - 1/b^2 `
`m' = m^2 `

Refer to the Keisan special function calculators for check values (https://keisan.casio.com/ : Home => Professional => Special Function => Elliptic Function). The Keisan functions use u and k instead of u and m.

Reference : Numerical Calculation of Elliptic Integrals and Elliptic Functions, R. Bulirsch, 1965

Change Module :

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