DLMF:22.13.E2 (Q7053)

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DLMF:22.13.E2
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    Statements

    Defining formula
    ( d d z ⁡ cn ⁡ ( z , k ) ) 2 = ( 1 - cn 2 ⁡ ( z , k ) ) ⁢ ( k ′ 2 + k 2 ⁢ cn 2 ⁡ ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-cn 𝑧 𝑘 2 1 Jacobi-elliptic-cn 2 𝑧 𝑘 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 Jacobi-elliptic-cn 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% cn}\left(z,k\right)\right)^{2}={\left(1-{\operatorname{cn}^{2}}\left(z,k\right% )\right)}{\left({k^{\prime}}^{2}+k^{2}{\operatorname{cn}^{2}}\left(z,k\right)% \right)},}}
    0 references
    DLMF id
    DLMF:22.13.E2
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.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.m2abdec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1bdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1bdec
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    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1adec
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