DLMF:22.13.E3 (Q7054)

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DLMF:22.13.E3
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    Statements

    Defining formula
    ( d d z ⁡ dn ⁡ ( z , k ) ) 2 = ( 1 - dn 2 ⁡ ( z , k ) ) ⁢ ( dn 2 ⁡ ( z , k ) - k ′ 2 ) . superscript derivative 𝑧 Jacobi-elliptic-dn 𝑧 𝑘 2 1 Jacobi-elliptic-dn 2 𝑧 𝑘 Jacobi-elliptic-dn 2 𝑧 𝑘 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% dn}\left(z,k\right)\right)^{2}=\left(1-{\operatorname{dn}^{2}}\left(z,k\right)% \right)\left({\operatorname{dn}^{2}}\left(z,k\right)-{k^{\prime}}^{2}\right).}}
    0 references
    DLMF id
    DLMF:22.13.E3
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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.m2aadec
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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.m2acdec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1cdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1cdec
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