DLMF:

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

Figure 22.3.24 (See in context.)

Figure 22.3.24: $\mathop{\mathrm{sn}\/}\nolimits\left(x+iy,k\right)$ for $-4\leq x\leq 4$ , $0\leq y\leq 8$ , $k=1+\tfrac{1}{2}i$ . $K=1.5149\ldots+i0.5235\dots$ , $K^{{\prime}}=1.4620\ldots-i0.3552\dots$ .

Annotations:

Symbols:: $\mathop{\mathrm{sn}\/}\nolimits\left(z,k\right)$ : Jacobian elliptic function, $\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ : Legendre’s complementary complete elliptic integral of the first kind, $\mathop{K\/}\nolimits\!\left(k\right)$ : Legendre’s complete elliptic integral of the first kind, : real, : real and : modulus
Keywords:: Jacobian elliptic functions
Permalink:: http://dlmf.nist.gov/22.3.F24.mag
Encodings:: Magnified png, VRML, X3D, 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