The Jacobi elliptic functions are standard forms of elliptic functions. The three basic functions are denoted cn(u, k), dn(u, k), and sn(u, k), where k is known as the elliptic modulus. They arise from the inversion of the elliptic integral of the first kind, u = F(ϕ, k) = integral_0^ϕ (d t)/sqrt(1 - k^2 sin^2 t), where 0
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