DLMF:22.6.E21 (Q6955)

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Language	Label	Description	Also known as
English	DLMF:22.6.E21	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\operatorname{dn}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{k^{2}\operatorname{cn}\left(z,k\right)+\operatorname{dn}\left(z,k% \right)+{k^{\prime}}^{2}}{1+\operatorname{dn}\left(z,k\right)}=\frac{{k^{% \prime}}^{2}(1-\operatorname{cn}\left(z,k\right))}{\operatorname{dn}\left(z,k% \right)-\operatorname{cn}\left(z,k\right)}=\frac{{k^{\prime}}^{2}(1+% \operatorname{dn}\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.E21

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Jacobian elliptic function

Defining formula

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

C22.S2.E5.m2ahdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E6.m2ahdec

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Defining formula

{\displaystyle{\displaystyle z}}

C22.S1.XMD3.m1tdec

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