DLMF:22.13.E4 (Q7055): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

cd ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellcdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E8.m2aadec

Revision as of 15:18, 2 January 2020

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DLMF:22.13.E4
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    ( d d z cd ( z , k ) ) 2 = ( 1 - cd 2 ( z , k ) ) ( 1 - k 2 cd 2 ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-cd 𝑧 𝑘 2 1 Jacobi-elliptic-cd 2 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-cd 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% cd}\left(z,k\right)\right)^{2}=\left(1-{\operatorname{cd}^{2}}\left(z,k\right)% \right)\left(1-k^{2}{\operatorname{cd}^{2}}\left(z,k\right)\right),}}
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    DLMF:22.13.E4
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    cd ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E8.m2aadec
    0 references