DLMF:22.6.E9 (Q6943)

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Language	Label	Description	Also known as
English	DLMF:22.6.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{sd}\left(2z,k\right)=\frac{2% \operatorname{sd}\left(z,k\right)\operatorname{cd}\left(z,k\right)% \operatorname{nd}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{% 4}}\left(z,k\right)},}}

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DLMF:22.6.E9

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Jacobian elliptic function

Defining formula

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

C22.S2.E8.m2abdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E6.m3abdec

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Jacobian elliptic function

Defining formula

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

C22.S2.E7.m2abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C22.S1.XMD3.m1hdec

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Sitelinks

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