DLMF:22.13.E8 (Q7059): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
test:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1edec

Latest revision as of 14:19, 2 January 2020

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DLMF:22.13.E8
No description defined

    Statements

    test
    ( d d z ⁡ nc ⁡ ( z , k ) ) 2 = ( k 2 + k ′ 2 ⁢ nc 2 ⁡ ( z , k ) ) ⁢ ( nc 2 ⁡ ( z , k ) - 1 ) , superscript derivative 𝑧 Jacobi-elliptic-nc 𝑧 𝑘 2 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nc 2 𝑧 𝑘 Jacobi-elliptic-nc 2 𝑧 𝑘 1 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% nc}\left(z,k\right)\right)^{2}={\left(k^{2}+{k^{\prime}}^{2}{\operatorname{nc}% ^{2}}\left(z,k\right)\right)}{\left({\operatorname{nc}^{2}}\left(z,k\right)-1% \right)},}}
    0 references
    DLMF id
    DLMF:22.13.E8
    0 references
    Symbols used
    Jacobian elliptic function
    test
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.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.m2ahdec
    0 references
    Q11985
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1hdec
    0 references
    Q11984
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1hdec
    0 references
    Q11988
    test
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1edec
    0 references
     
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