DLMF:22.8.E6 (Q6971)

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DLMF:22.8.E6
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    nd ( u + v ) = nd u nd v + k 2 sd u cd u sd v cd v 1 + k 2 k 2 sd 2 u sd 2 v , Jacobi-elliptic-nd 𝑢 𝑣 𝑘 Jacobi-elliptic-nd 𝑢 𝑘 Jacobi-elliptic-nd 𝑣 𝑘 superscript 𝑘 2 Jacobi-elliptic-sd 𝑢 𝑘 Jacobi-elliptic-cd 𝑢 𝑘 Jacobi-elliptic-sd 𝑣 𝑘 Jacobi-elliptic-cd 𝑣 𝑘 1 superscript 𝑘 2 superscript superscript 𝑘 2 Jacobi-elliptic-sd 2 𝑢 𝑘 Jacobi-elliptic-sd 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{nd}(u+v)=\frac{\operatorname{nd}u% \operatorname{nd}v+k^{2}\operatorname{sd}u\operatorname{cd}u\operatorname{sd}v% \operatorname{cd}v}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{2}}u{% \operatorname{sd}^{2}}v},}}
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    cd ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E8.m2abdec
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