DLMF:22.13.E9 (Q7060)

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DLMF:22.13.E9
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    Statements

    Defining formula
    ( d d z ⁡ sc ⁡ ( z , k ) ) 2 = ( 1 + sc 2 ⁡ ( z , k ) ) ⁢ ( 1 + k ′ 2 ⁢ sc 2 ⁡ ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-sc 𝑧 𝑘 2 1 Jacobi-elliptic-sc 2 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% sc}\left(z,k\right)\right)^{2}=\left(1+{\operatorname{sc}^{2}}\left(z,k\right)% \right)\left(1+{k^{\prime}}^{2}{\operatorname{sc}^{2}}\left(z,k\right)\right),}}
    0 references
    DLMF id
    DLMF:22.13.E9
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.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.m2aidec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1idec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1idec
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    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1fdec
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