DLMF:22.12.E5 (Q7043)

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DLMF:22.12.E5
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    Defining formula
    2 ⁢ K ⁢ k ⁢ cd ⁡ ( 2 ⁢ K ⁢ t , k ) = ∑ n = - ∞ ∞ π sin ⁡ ( π ⁢ ( t + 1 2 - ( n + 1 2 ) ⁢ τ ) ) = ∑ n = - ∞ ∞ ( ∑ m = - ∞ ∞ ( - 1 ) m t + 1 2 - m - ( n + 1 2 ) ⁢ τ ) , 2 𝐾 𝑘 Jacobi-elliptic-cd 2 𝐾 𝑡 𝑘 superscript subscript 𝑛 𝜋 𝜋 𝑡 1 2 𝑛 1 2 𝜏 superscript subscript 𝑛 superscript subscript 𝑚 superscript 1 𝑚 𝑡 1 2 𝑚 𝑛 1 2 𝜏 {\displaystyle{\displaystyle 2Kk\operatorname{cd}\left(2Kt,k\right)=\sum_{n=-% \infty}^{\infty}\frac{\pi}{\sin\left(\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)% \right)}=\sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m% }}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right),}}
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    DLMF id
    DLMF:22.12.E5
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