# DLMF:22.6.E20 (Q6954)

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DLMF:22.6.E20
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## Statements

${\displaystyle{\displaystyle{\operatorname{cn}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{-{k^{\prime}}^{2}+\operatorname{dn}\left(z,k\right)+k^{2}\operatorname% {cn}\left(z,k\right)}{k^{2}(1+\operatorname{cn}\left(z,k\right))}=\frac{{k^{% \prime}}^{2}(1-\operatorname{dn}\left(z,k\right))}{k^{2}(\operatorname{dn}% \left(z,k\right)-\operatorname{cn}\left(z,k\right))}=\frac{{k^{\prime}}^{2}(1+% \operatorname{cn}\left(z,k\right))}{{k^{\prime}}^{2}+\operatorname{dn}\left(z,% k\right)-k^{2}\operatorname{cn}\left(z,k\right)},}}$
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DLMF:22.6.E20
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${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$
C22.S2.E5.m2agdec
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${\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}$
C22.S2.E6.m2agdec
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${\displaystyle{\displaystyle z}}$
C22.S1.XMD3.m1sdec
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${\displaystyle{\displaystyle k}}$
C22.S1.XMD4.m1sdec
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${\displaystyle{\displaystyle k^{\prime}}}$
C22.S1.XMD5.m1mdec
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