DLMF:22.11.E8 (Q7032): 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:

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

\Jacobielldsk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E7.m3adec

Revision as of 15:13, 2 January 2020

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DLMF:22.11.E8
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    Statements

    ds ( z , k ) - π 2 K csc ζ = - 2 π K n = 0 q 2 n + 1 sin ( ( 2 n + 1 ) ζ ) 1 + q 2 n + 1 , Jacobi-elliptic-ds 𝑧 𝑘 𝜋 2 𝐾 𝜁 2 𝜋 𝐾 superscript subscript 𝑛 0 superscript 𝑞 2 𝑛 1 2 𝑛 1 𝜁 1 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{ds}\left(z,k\right)-\frac{\pi}{2K}% \csc\zeta=-\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin\left((2n+1)% \zeta\right)}{1+q^{2n+1}},}}
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    DLMF:22.11.E8
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    ds ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m3adec
    0 references