DLMF:22.8.E21 (Q6986)

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DLMF:22.8.E21
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    Statements

    Defining formula
    k ′ 2 - k ′ 2 ⁢ k 2 ⁢ sn ⁡ z 1 ⁢ sn ⁡ z 2 ⁢ sn ⁡ z 3 ⁢ sn ⁡ z 4 + k 2 ⁢ cn ⁡ z 1 ⁢ cn ⁡ z 2 ⁢ cn ⁡ z 3 ⁢ cn ⁡ z 4 - dn ⁡ z 1 ⁢ dn ⁡ z 2 ⁢ dn ⁡ z 3 ⁢ dn ⁡ z 4 = 0 . superscript superscript 𝑘 ′ 2 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 Jacobi-elliptic-sn subscript 𝑧 1 𝑘 Jacobi-elliptic-sn subscript 𝑧 2 𝑘 Jacobi-elliptic-sn subscript 𝑧 3 𝑘 Jacobi-elliptic-sn subscript 𝑧 4 𝑘 superscript 𝑘 2 Jacobi-elliptic-cn subscript 𝑧 1 𝑘 Jacobi-elliptic-cn subscript 𝑧 2 𝑘 Jacobi-elliptic-cn subscript 𝑧 3 𝑘 Jacobi-elliptic-cn subscript 𝑧 4 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 Jacobi-elliptic-dn subscript 𝑧 4 𝑘 0 {\displaystyle{\displaystyle{k^{\prime}}^{2}-{k^{\prime}}^{2}k^{2}% \operatorname{sn}z_{1}\operatorname{sn}z_{2}\operatorname{sn}z_{3}% \operatorname{sn}z_{4}+k^{2}\operatorname{cn}z_{1}\operatorname{cn}z_{2}% \operatorname{cn}z_{3}\operatorname{cn}z_{4}-\operatorname{dn}z_{1}% \operatorname{dn}z_{2}\operatorname{dn}z_{3}\operatorname{dn}z_{4}=0.}}
    0 references
    DLMF id
    DLMF:22.8.E21
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2ajdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2ajdec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2ajdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1bdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1adec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1dec
    0 references
     
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