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Statements
x
=
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sn
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sn
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sn
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sn
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2
cn
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cn
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cn
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cn
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dn
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dn
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dn
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dn
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,
𝑥
superscript
𝑘
2
Jacobi-elliptic-sn
𝑧
𝑘
Jacobi-elliptic-sn
subscript
𝑧
1
𝑘
Jacobi-elliptic-sn
subscript
𝑧
2
𝑘
Jacobi-elliptic-sn
subscript
𝑧
3
𝑘
superscript
𝑘
2
superscript
superscript
𝑘
′
2
Jacobi-elliptic-cn
𝑧
𝑘
Jacobi-elliptic-cn
subscript
𝑧
1
𝑘
Jacobi-elliptic-cn
subscript
𝑧
2
𝑘
Jacobi-elliptic-cn
subscript
𝑧
3
𝑘
1
superscript
superscript
𝑘
′
2
Jacobi-elliptic-dn
𝑧
𝑘
Jacobi-elliptic-dn
subscript
𝑧
1
𝑘
Jacobi-elliptic-dn
subscript
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2
𝑘
Jacobi-elliptic-dn
subscript
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3
𝑘
{\displaystyle{\displaystyle x=k^{2}\operatorname{sn}\left(z,k\right)%
\operatorname{sn}\left(z_{1},k\right)\operatorname{sn}\left(z_{2},k\right)%
\operatorname{sn}\left(z_{3},k\right)-\frac{k^{2}}{{k^{\prime}}^{2}}%
\operatorname{cn}\left(z,k\right)\operatorname{cn}\left(z_{1},k\right)%
\operatorname{cn}\left(z_{2},k\right)\operatorname{cn}\left(z_{3},k\right)+%
\frac{1}{{k^{\prime}}^{2}}\operatorname{dn}\left(z,k\right)\operatorname{dn}%
\left(z_{1},k\right)\operatorname{dn}\left(z_{2},k\right)\operatorname{dn}%
\left(z_{3},k\right),}}
cn
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z
,
k
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Jacobi-elliptic-cn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
dn
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z
,
k
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Jacobi-elliptic-dn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
sn
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z
,
k
)
Jacobi-elliptic-sn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
