DLMF:22.13.E18 (Q7069)

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DLMF:22.13.E18
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    Statements

    Defining formula
    d 2 d z 2 ⁡ nd ⁡ ( z , k ) = ( 1 + k ′ 2 ) ⁢ nd ⁡ ( z , k ) - 2 ⁢ k ′ 2 ⁢ nd 3 ⁡ ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-nd 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nd 𝑧 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nd 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{nd}\left(z,k\right)=(1+{k^{\prime}}^{2})\operatorname{nd}\left(z% ,k\right)-2{k^{\prime}}^{2}{\operatorname{nd}^{3}}\left(z,k\right),}}
    0 references
    DLMF id
    DLMF:22.13.E18
    0 references
    Symbols used
    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.m3abdec
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    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.m2ardec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1rdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1rdec
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    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1ldec
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