DLMF:22.8.E25 (Q6990)

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DLMF:22.8.E25
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    Statements

    Defining formula
    ( dn ⁡ z 2 + dn ⁡ z 3 ) ⁢ ( dn ⁡ z 3 + dn ⁡ z 1 ) ⁢ ( dn ⁡ z 1 + dn ⁡ z 2 ) dn ⁡ z 1 + dn ⁡ z 2 + dn ⁡ z 3 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 {\displaystyle{\displaystyle\frac{(\operatorname{dn}z_{2}+\operatorname{dn}z_{% 3})(\operatorname{dn}z_{3}+\operatorname{dn}z_{1})(\operatorname{dn}z_{1}+% \operatorname{dn}z_{2})}{\operatorname{dn}z_{1}+\operatorname{dn}z_{2}+% \operatorname{dn}z_{3}}}}
    0 references
    DLMF id
    DLMF:22.8.E25
    0 references
    Symbols used
    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.m2aldec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1fdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1edec
    0 references
     
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