DLMF:22.8.E10 (Q6975)

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DLMF:22.8.E10
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    Statements

    Defining formula
    ns ⁡ ( u + v ) = ns ⁡ u ⁢ ds ⁡ v ⁢ cs ⁡ v - ns ⁡ v ⁢ ds ⁡ u ⁢ cs ⁡ u cs 2 ⁡ v - cs 2 ⁡ u , Jacobi-elliptic-ns 𝑢 𝑣 𝑘 Jacobi-elliptic-ns 𝑢 𝑘 Jacobi-elliptic-ds 𝑣 𝑘 Jacobi-elliptic-cs 𝑣 𝑘 Jacobi-elliptic-ns 𝑣 𝑘 Jacobi-elliptic-ds 𝑢 𝑘 Jacobi-elliptic-cs 𝑢 𝑘 Jacobi-elliptic-cs 2 𝑣 𝑘 Jacobi-elliptic-cs 2 𝑢 𝑘 {\displaystyle{\displaystyle\operatorname{ns}(u+v)=\frac{\operatorname{ns}u% \operatorname{ds}v\operatorname{cs}v-\operatorname{ns}v\operatorname{ds}u% \operatorname{cs}u}{{\operatorname{cs}^{2}}v-{\operatorname{cs}^{2}}u},}}
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    DLMF id
    DLMF:22.8.E10
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