DLMF:22.8.E13 (Q6978)

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DLMF:22.8.E13
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    Statements

    Defining formula
    sn ⁡ ( u + v ) = sn 2 ⁡ u - sn 2 ⁡ v sn ⁡ u ⁢ cn ⁡ v ⁢ dn ⁡ v - sn ⁡ v ⁢ cn ⁡ u ⁢ dn ⁡ u , Jacobi-elliptic-sn 𝑢 𝑣 𝑘 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 {\displaystyle{\displaystyle\operatorname{sn}(u+v)=\frac{{\operatorname{sn}^{2% }}u-{\operatorname{sn}^{2}}v}{\operatorname{sn}u\operatorname{cn}v% \operatorname{dn}v-\operatorname{sn}v\operatorname{cn}u\operatorname{dn}u},}}
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    DLMF id
    DLMF:22.8.E13
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