DLMF:22.13.E13 (Q7064)

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DLMF:22.13.E13
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    Statements

    Defining formula
    d 2 d z 2 ⁡ sn ⁡ ( z , k ) = - ( 1 + k 2 ) ⁢ sn ⁡ ( z , k ) + 2 ⁢ k 2 ⁢ sn 3 ⁡ ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-sn 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 𝑧 𝑘 2 superscript 𝑘 2 Jacobi-elliptic-sn 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{sn}\left(z,k\right)=-(1+k^{2})\operatorname{sn}\left(z,k\right)+% 2k^{2}{\operatorname{sn}^{3}}\left(z,k\right),}}
    0 references
    DLMF id
    DLMF:22.13.E13
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2abdec
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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.m2amdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1mdec
    0 references
     
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