DLMF:22.13.E3 (Q7054)

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DLMF:22.13.E3
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    Statements

    test
    ( 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
    0 references
    Symbols used
    Jacobian elliptic function
    test
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aadec
    0 references
     
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