English: Plot of the degenerate Jacobi curve (x^2+y^2/b^2=1, b=infinity) and the twelve Jacobi Elliptic functions pq(u,1) for a particular value of angle φ. The solid curve is the degenerate ellipse, with m=1 and u=F(φ,1) where F(.,.) is the elliptic integral of the first kind. Since these are the Jacobi functions for m=0 (circular trigonometric functions) but with imaginary arguments, they correspond to the six hyperbolic trigonometric functions.
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