DLMF:22.6.E7 (Q6941): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:22.6.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{dn}\left(2z,k\right)=\frac{{% \operatorname{dn}^{2}}\left(z,k\right)-k^{2}{\operatorname{sn}^{2}}\left(z,k% \right){\operatorname{cn}^{2}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}% \left(z,k\right)}=\frac{{\operatorname{dn}^{4}}\left(z,k\right)+k^{2}{k^{% \prime}}^{2}{\operatorname{sn}^{4}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}% ^{4}}\left(z,k\right)}.}}

0 references

DLMF:22.6.E7

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Jacobian elliptic function

Defining formula

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

C22.S2.E5.m2acdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E6.m2acdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E4.m2acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C22.S1.XMD3.m1fdec

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