DLMF:22.8.E16 (Q6981)

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DLMF:22.8.E16
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    cn ( u + v ) = 1 - sn 2 u - sn 2 v + k 2 sn 2 u sn 2 v cn u cn v + sn u dn u sn v dn v , Jacobi-elliptic-cn 𝑢 𝑣 𝑘 1 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{cn}(u+v)=\frac{1-{\operatorname{sn}^% {2}}u-{\operatorname{sn}^{2}}v+k^{2}{\operatorname{sn}^{2}}u{\operatorname{sn}% ^{2}}v}{\operatorname{cn}u\operatorname{cn}v+\operatorname{sn}u\operatorname{% dn}u\operatorname{sn}v\operatorname{dn}v},}}
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    DLMF:22.8.E16
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