Graphs of Elliptic Functions

Illustration The following is a graph showing the three elliptic functions of Jacobi. Here the value of tau=.8i for the theta functions used to define sn(z), cn(z) and dn(z). The parameter k=.8541

Note that cn(z) is not a translate of sn(z).

As tau increases the Jacobi functions look more like sine and cosine, and dn looks like 1. Here are the graphs for tau=1.5i. The parameter k=.3659

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