DLMF:22.7.E4 (Q6960)

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DLMF:22.7.E4
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    Statements

    Defining formula
    dn ⁡ ( z , k ) = dn 2 ⁡ ( z / ( 1 + k 1 ) , k 1 ) - ( 1 - k 1 ) 1 + k 1 - dn 2 ⁡ ( z / ( 1 + k 1 ) , k 1 ) . Jacobi-elliptic-dn 𝑧 𝑘 Jacobi-elliptic-dn 2 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 1 subscript 𝑘 1 1 subscript 𝑘 1 Jacobi-elliptic-dn 2 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{dn}\left(z,k\right)=\frac{{% \operatorname{dn}^{2}}\left(z/(1+k_{1}),k_{1}\right)-(1-k_{1})}{1+k_{1}-{% \operatorname{dn}^{2}}\left(z/(1+k_{1}),k_{1}\right)}.}}
    0 references
    DLMF id
    DLMF:22.7.E4
    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.m2aadec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1bdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1bdec
    0 references
     
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