DLMF:22.13.E15 (Q7066)

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DLMF:22.13.E15
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    Statements

    Defining formula
    d 2 d z 2 ⁡ dn ⁡ ( z , k ) = ( 1 + k ′ 2 ) ⁢ dn ⁡ ( z , k ) - 2 ⁢ dn 3 ⁡ ( z , k ) . derivative 𝑧 2 Jacobi-elliptic-dn 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-dn 𝑧 𝑘 2 Jacobi-elliptic-dn 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{dn}\left(z,k\right)=(1+{k^{\prime}}^{2})\operatorname{dn}\left(z% ,k\right)-2{\operatorname{dn}^{3}}\left(z,k\right).}}
    0 references
    DLMF id
    DLMF:22.13.E15
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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
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aodec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1odec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1odec
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