DLMF:22.17.E8 (Q7163)

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DLMF:22.17.E8
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    Statements

    Defining formula
    dn ⁡ ( z , i ⁢ k ) = nd ⁡ ( z / k 1 ′ , k 1 ) . Jacobi-elliptic-dn 𝑧 𝑖 𝑘 Jacobi-elliptic-nd 𝑧 superscript subscript 𝑘 1 ′ subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{dn}\left(z,ik\right)=\operatorname{% nd}\left(z/k_{1}^{\prime},k_{1}\right).}}
    0 references
    DLMF id
    DLMF:22.17.E8
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    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.m2abdec
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    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.m3adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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