DLMF:

Figure 22.3.2 (See in context.)

Figure 22.3.2: $k=0.7$ , $-3K\leq x\leq 3K$ , $K=1.8456\dots$ . For $\mathop{\mathrm{cn}\/}\nolimits\left(x,k\right)$ the curve for $k=1/\sqrt{2}=0.70710\dots$ is a boundary between the curves that have an inflection point in the interval $0\leq x\leq 2\!\mathop{K\/}\nolimits\!\left(k\right)$ , and its translates, and those that do not; see Walker (1996, p. 146).

Annotations:

Symbols:: $\mathop{\mathrm{cn}\/}\nolimits\left(z,k\right)$ : Jacobian elliptic function, $\mathop{K\/}\nolimits\!\left(k\right)$ : Legendre’s complete elliptic integral of the first kind, $x$ : real and $k$ : modulus
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