DLMF:22.8.E11 (Q6976)

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DLMF:22.8.E11
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    Statements

    Defining formula
    ds ⁡ ( u + v ) = ds ⁡ u ⁢ cs ⁡ v ⁢ ns ⁡ v - ds ⁡ v ⁢ cs ⁡ u ⁢ ns ⁡ u cs 2 ⁡ v - cs 2 ⁡ u , Jacobi-elliptic-ds 𝑢 𝑣 𝑘 Jacobi-elliptic-ds 𝑢 𝑘 Jacobi-elliptic-cs 𝑣 𝑘 Jacobi-elliptic-ns 𝑣 𝑘 Jacobi-elliptic-ds 𝑣 𝑘 Jacobi-elliptic-cs 𝑢 𝑘 Jacobi-elliptic-ns 𝑢 𝑘 Jacobi-elliptic-cs 2 𝑣 𝑘 Jacobi-elliptic-cs 2 𝑢 𝑘 {\displaystyle{\displaystyle\operatorname{ds}(u+v)=\frac{\operatorname{ds}u% \operatorname{cs}v\operatorname{ns}v-\operatorname{ds}v\operatorname{cs}u% \operatorname{ns}u}{{\operatorname{cs}^{2}}v-{\operatorname{cs}^{2}}u},}}
    0 references
    DLMF id
    DLMF:22.8.E11
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cs ⁡ ( z , k ) Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m3aadec
    0 references
    Jacobian elliptic function
    Defining formula
    ds ⁡ ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m3aadec
    0 references
    Jacobian elliptic function
    Defining formula
    ns ⁡ ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m3aadec
    0 references
    Q11991
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1jdec
    0 references
     
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