DLMF:22.11.E1 (Q7025)

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DLMF:22.11.E1
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    Defining formula
    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 id
    DLMF:22.11.E1
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