DLMF:22.13.E6 (Q7057): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1fdec

Revision as of 15:19, 2 January 2020

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DLMF:22.13.E6
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    Statements

    ( d d z nd ( z , k ) ) 2 = ( nd 2 ( z , k ) - 1 ) ( 1 - k 2 nd 2 ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-nd 𝑧 𝑘 2 Jacobi-elliptic-nd 2 𝑧 𝑘 1 1 superscript superscript 𝑘 2 Jacobi-elliptic-nd 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% nd}\left(z,k\right)\right)^{2}=\left({\operatorname{nd}^{2}}\left(z,k\right)-1% \right)\left(1-{k^{\prime}}^{2}{\operatorname{nd}^{2}}\left(z,k\right)\right),}}
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    DLMF:22.13.E6
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    nd ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m3aadec
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2afdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1fdec
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