DLMF:

22 Jacobian Elliptic Functions Properties 22.3 Graphics 22.3 Graphics 22.4 Periods, Poles, and Zeros

Figure 22.3.2 (See in context.)

Figure 22.3.2:

, $-3K\leq x\leq 3K$ , $K=1.8456\dots$ . 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, : real and : modulus
Permalink:: http://dlmf.nist.gov/22.3.F2.mag
Encodings:: Magnified png, pdf

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 22.3 Graphics 22.4 Periods, Poles, and Zeros