DLMF:22.11.E6 (Q7030): 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:

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

\Jacobiellndk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m3adec

Revision as of 15:12, 2 January 2020

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DLMF:22.11.E6
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    Statements

    nd ( z , k ) = π 2 K k + 2 π K k n = 1 ( - 1 ) n q n cos ( 2 n ζ ) 1 + q 2 n . Jacobi-elliptic-nd 𝑧 𝑘 𝜋 2 𝐾 superscript 𝑘 2 𝜋 𝐾 superscript 𝑘 superscript subscript 𝑛 1 superscript 1 𝑛 superscript 𝑞 𝑛 2 𝑛 𝜁 1 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle\operatorname{nd}\left(z,k\right)=\frac{\pi}{2Kk^{% \prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos% \left(2n\zeta\right)}{1+q^{2n}}.}}
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    DLMF:22.11.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.m3adec
    0 references