DLMF:22.11.E1 (Q7025): 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.m1dec

Revision as of 15:11, 2 January 2020

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DLMF:22.11.E1
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    Statements

    sn ( z , k ) = 2 π K k n = 0 q n + 1 2 sin ( ( 2 n + 1 ) ζ ) 1 - q 2 n + 1 , Jacobi-elliptic-sn 𝑧 𝑘 2 𝜋 𝐾 𝑘 superscript subscript 𝑛 0 superscript 𝑞 𝑛 1 2 2 𝑛 1 𝜁 1 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{sn}\left(z,k\right)=\frac{2\pi}{Kk}% \sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin\left((2n+1)\zeta\right)}{1-q^{2% n+1}},}}
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    DLMF:22.11.E1
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1adec
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    q 𝑞 {\displaystyle{\displaystyle q}}
    C22.S2.E1.m2adec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1dec
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