DLMF:22.11.E5 (Q7029): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobiellsdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E7.m2adec

Revision as of 15:12, 2 January 2020

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DLMF:22.11.E5
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    sd ( z , k ) = 2 π K k k n = 0 ( - 1 ) n q n + 1 2 sin ( ( 2 n + 1 ) ζ ) 1 + q 2 n + 1 , Jacobi-elliptic-sd 𝑧 𝑘 2 𝜋 𝐾 𝑘 superscript 𝑘 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝑞 𝑛 1 2 2 𝑛 1 𝜁 1 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{sd}\left(z,k\right)=\frac{2\pi}{Kkk^% {\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin\left((2n+1)% \zeta\right)}{1+q^{2n+1}},}}
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    sd ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m2adec
    0 references