DLMF:20.5.E15 (Q6782)

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DLMF:20.5.E15
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    Defining formula
    θ 2 ⁡ ( z | τ ) = θ 2 ⁡ ( 0 | τ ) ⁢ lim N → ∞ ⁡ ∏ n = - N N lim M → ∞ ⁡ ∏ m = 1 - M M ( 1 + z ( m - 1 2 + n ⁢ τ ) ⁢ π ) , Jacobi-theta-tau 2 𝑧 𝜏 Jacobi-theta-tau 2 0 𝜏 subscript → 𝑁 superscript subscript product 𝑛 𝑁 𝑁 subscript → 𝑀 superscript subscript product 𝑚 1 𝑀 𝑀 1 𝑧 𝑚 1 2 𝑛 𝜏 𝜋 {\displaystyle{\displaystyle\theta_{2}\left(z\middle|\tau\right)=\theta_{2}% \left(0\middle|\tau\right)\*\lim_{N\to\infty}\prod_{n=-N}^{N}\lim_{M\to\infty}% \prod_{m=1-M}^{M}\left(1+\frac{z}{(m-\tfrac{1}{2}+n\tau)\pi}\right),}}
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    DLMF id
    DLMF:20.5.E15
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