# DLMF:29.8.E1 (Q8704)

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DLMF:29.8.E1
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## Statements

${\displaystyle{\displaystyle x=k^{2}\operatorname{sn}\left(z,k\right)% \operatorname{sn}\left(z_{1},k\right)\operatorname{sn}\left(z_{2},k\right)% \operatorname{sn}\left(z_{3},k\right)-\frac{k^{2}}{{k^{\prime}}^{2}}% \operatorname{cn}\left(z,k\right)\operatorname{cn}\left(z_{1},k\right)% \operatorname{cn}\left(z_{2},k\right)\operatorname{cn}\left(z_{3},k\right)+% \frac{1}{{k^{\prime}}^{2}}\operatorname{dn}\left(z,k\right)\operatorname{dn}% \left(z_{1},k\right)\operatorname{dn}\left(z_{2},k\right)\operatorname{dn}% \left(z_{3},k\right),}}$
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DLMF:29.8.E1
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${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$
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${\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}$
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${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$
${\displaystyle{\displaystyle x}}$
${\displaystyle{\displaystyle z}}$
${\displaystyle{\displaystyle k}}$