DLMF:22.6.E19 (Q6953)

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Language	Label	Description	Also known as
English	DLMF:22.6.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\operatorname{sn}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{1-\operatorname{cn}\left(z,k\right)}{1+\operatorname{dn}\left(z,k% \right)}=\frac{1-\operatorname{dn}\left(z,k\right)}{k^{2}(1+\operatorname{cn}% \left(z,k\right))}=\frac{\operatorname{dn}\left(z,k\right)-k^{2}\operatorname{% cn}\left(z,k\right)-{k^{\prime}}^{2}}{k^{2}(\operatorname{dn}\left(z,k\right)-% \operatorname{cn}\left(z,k\right))},}}

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DLMF:22.6.E19

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E5.m2afdec

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E6.m2afdec

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E4.m2afdec

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Defining formula

{\displaystyle{\displaystyle z}}

C22.S1.XMD3.m1rdec

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Defining formula

{\displaystyle{\displaystyle k}}

C22.S1.XMD4.m1rdec

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