DLMF:22.13.E10 (Q7061)

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DLMF:22.13.E10
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    Statements

    test
    ( d d z ⁡ ns ⁡ ( z , k ) ) 2 = ( ns 2 ⁡ ( z , k ) - k 2 ) ⁢ ( ns 2 ⁡ ( z , k ) - 1 ) , superscript derivative 𝑧 Jacobi-elliptic-ns 𝑧 𝑘 2 Jacobi-elliptic-ns 2 𝑧 𝑘 superscript 𝑘 2 Jacobi-elliptic-ns 2 𝑧 𝑘 1 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% ns}\left(z,k\right)\right)^{2}=\left({\operatorname{ns}^{2}}\left(z,k\right)-k% ^{2}\right)\left({\operatorname{ns}^{2}}\left(z,k\right)-1\right),}}
    0 references
    DLMF id
    DLMF:22.13.E10
    0 references
    Symbols used
    Jacobian elliptic function
    test
    ns ⁡ ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m3aadec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2ajdec
    0 references
    Q11985
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1jdec
    0 references
     
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