DLMF:22.8.E6 (Q6971)

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DLMF:22.8.E6
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    Statements

    Defining formula
    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},}}
    0 references
    DLMF id
    DLMF:22.8.E6
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m3abdec
    0 references
    Jacobian elliptic function
    Defining formula
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2abdec
    0 references
    Q11991
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1edec
    0 references
    Q11992
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD2.m1edec
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    Q11993
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD3.m1edec
    0 references
     
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