DLMF:22.8.E4 (Q6969)

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Language	Label	Description	Also known as
English	DLMF:22.8.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{cd}(u+v)=\frac{\operatorname{cd}u% \operatorname{cd}v-{k^{\prime}}^{2}\operatorname{sd}u\operatorname{nd}u% \operatorname{sd}v\operatorname{nd}v}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd% }^{2}}u{\operatorname{sd}^{2}}v},}}

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DLMF:22.8.E4

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Jacobian elliptic function

Defining formula

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

C22.S2.E8.m2adec

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Jacobian elliptic function

Defining formula

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

C22.S2.E6.m3adec

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Jacobian elliptic function

Defining formula

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

C22.S2.E7.m2adec

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Defining formula

{\displaystyle{\displaystyle u}}

C22.S8.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle v}}

C22.S8.XMD2.m1cdec

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