DLMF:22.11.E12 (Q7036)

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DLMF:22.11.E12
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    Defining formula
    sc ⁡ ( z , k ) - π 2 ⁢ K ⁢ k ′ ⁢ tan ⁡ ζ = 2 ⁢ π K ⁢ k ′ ⁢ ∑ n = 1 ∞ ( - 1 ) n ⁢ q 2 ⁢ n ⁢ sin ⁡ ( 2 ⁢ n ⁢ ζ ) 1 + q 2 ⁢ n . Jacobi-elliptic-sc 𝑧 𝑘 𝜋 2 𝐾 superscript 𝑘 ′ 𝜁 2 𝜋 𝐾 superscript 𝑘 ′ superscript subscript 𝑛 1 superscript 1 𝑛 superscript 𝑞 2 𝑛 2 𝑛 𝜁 1 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle\operatorname{sc}\left(z,k\right)-\frac{\pi}{2Kk^{% \prime}}\tan\zeta=\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{% 2n}\sin\left(2n\zeta\right)}{1+q^{2n}}.}}
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    DLMF id
    DLMF:22.11.E12
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