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DLMF:22.13.E20 - MaRDI portal

DLMF:22.13.E20 (Q7764)

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DLMF:22.13.E20
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    Statements

    DLMF defining formula
    d 2 d z 2 ⁡ nc ⁡ ( z , k ) = ( k 2 - k ′ 2 ) ⁢ nc ⁡ ( z , k ) + 2 ⁢ k ′ 2 ⁢ nc 3 ⁡ ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-nc 𝑧 𝑘 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nc 𝑧 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nc 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{nc}\left(z,k\right)=(k^{2}-{k^{\prime}}^{2})\operatorname{nc}% \left(z,k\right)+2{k^{\prime}}^{2}{\operatorname{nc}^{3}}\left(z,k\right),}}
    0 references
    Symbols used
    Jacobian elliptic function
    DLMF defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3abdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    DLMF 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.m2atdec
    0 references
    complex
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1tdec
    0 references
    modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1tdec
    0 references
    complementary modulus
    DLMF defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1mdec
    0 references

    Identifiers

     
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