DLMF: Figure 22.3.24 ‣ §22.3 Graphics ‣ Properties ‣ Chapter 22 Jacobian Elliptic Functions

Figure 22.3.24 (See in context.)

Figure 22.3.24:

\operatorname{sn}\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

ⓘ

Symbols:: $\operatorname{sn}\left(\NVar{z},\NVar{k}\right)$ : Jacobian elliptic function, ${K^{\prime}}\left(\NVar{k}\right)$ : Legendre’s complementary complete elliptic integral of the first kind, $K\left(\NVar{k}\right)$ : Legendre’s complete elliptic integral of the first kind, $\mathrm{i}$ : imaginary unit, $x$ : real, $y$ : real and $k$ : modulus
Keywords:: Jacobian elliptic functions, complex, modulus
Permalink:: http://dlmf.nist.gov/22.3.F24.viz