DLMF:22.8.E8 (Q6973)

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DLMF:22.8.E8
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    Statements

    Defining formula
    nc ⁡ ( u + v ) = nc ⁡ u ⁢ nc ⁡ v + sc ⁡ u ⁢ dc ⁡ u ⁢ sc ⁡ v ⁢ dc ⁡ v 1 - k ′ 2 ⁢ sc 2 ⁡ u ⁢ sc 2 ⁡ v , Jacobi-elliptic-nc 𝑢 𝑣 𝑘 Jacobi-elliptic-nc 𝑢 𝑘 Jacobi-elliptic-nc 𝑣 𝑘 Jacobi-elliptic-sc 𝑢 𝑘 Jacobi-elliptic-dc 𝑢 𝑘 Jacobi-elliptic-sc 𝑣 𝑘 Jacobi-elliptic-dc 𝑣 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 2 𝑢 𝑘 Jacobi-elliptic-sc 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{nc}(u+v)=\frac{\operatorname{nc}u% \operatorname{nc}v+\operatorname{sc}u\operatorname{dc}u\operatorname{sc}v% \operatorname{dc}v}{1-{k^{\prime}}^{2}{\operatorname{sc}^{2}}u{\operatorname{% sc}^{2}}v},}}
    0 references
    DLMF id
    DLMF:22.8.E8
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3aadec
    0 references
    Jacobian elliptic function
    Defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3aadec
    0 references
    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2aadec
    0 references
     
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