DLMF:22.12.E12 (Q7050): Difference between revisions

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

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2agdec

Revision as of 15:17, 2 January 2020

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DLMF:22.12.E12
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    Statements

    2 K ds ( 2 K t , k ) = n = - ( - 1 ) n π sin ( π ( t - n τ ) ) = n = - ( m = - ( - 1 ) m + n t - m - n τ ) , 2 𝐾 Jacobi-elliptic-ds 2 𝐾 𝑡 𝑘 superscript subscript 𝑛 superscript 1 𝑛 𝜋 𝜋 𝑡 𝑛 𝜏 superscript subscript 𝑛 superscript subscript 𝑚 superscript 1 𝑚 𝑛 𝑡 𝑚 𝑛 𝜏 {\displaystyle{\displaystyle 2K\operatorname{ds}\left(2Kt,k\right)=\sum_{n=-% \infty}^{\infty}\frac{(-1)^{n}\pi}{\sin\left(\pi(t-n\tau)\right)}=\sum_{n=-% \infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-n\tau}% \right),}}
    0 references
    DLMF:22.12.E12
    0 references
    ds ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m3adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2ajdec
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    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1akdec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2agdec
    0 references