DLMF: Figure 22.3.19 ‣ §22.3 Graphics ‣ Properties ‣ Chapter 22 Jacobian Elliptic Functions

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DLMF: Figure 22.3.19 ‣ §22.3 Graphics ‣ Properties ‣ Chapter 22 Jacobian Elliptic Functions

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

Figure 22.3.19 (See in context.)

Figure 22.3.19:

\operatorname{cd}\left(x+iy,k\right)

for

k=0.99

,

-3K\leq x\leq 3K

,

0\leq y\leq 4K^{\prime}

.

K=3.3566\dots

,

K^{\prime}=1.5786\dots

.

ⓘ

Annotations:

Symbols:: $\operatorname{cd}\left(\NVar{z},\NVar{k}\right)$ : 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
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22.3 Graphics 22.4 Periods, Poles, and Zeros

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