DLMF:20.5.E16 (Q6783)

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DLMF:20.5.E16
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    θ 3 ( z | τ ) = θ 3 ( 0 | τ ) lim N n = 1 - N N lim M m = 1 - M M ( 1 + z ( m - 1 2 + ( n - 1 2 ) τ ) π ) , Jacobi-theta-tau 3 𝑧 𝜏 Jacobi-theta-tau 3 0 𝜏 subscript 𝑁 superscript subscript product 𝑛 1 𝑁 𝑁 subscript 𝑀 superscript subscript product 𝑚 1 𝑀 𝑀 1 𝑧 𝑚 1 2 𝑛 1 2 𝜏 𝜋 {\displaystyle{\displaystyle\theta_{3}\left(z\middle|\tau\right)=\theta_{3}% \left(0\middle|\tau\right)\*\lim_{N\to\infty}\prod_{n=1-N}^{N}\lim_{M\to\infty% }\prod_{m=1-M}^{M}\left(1+\frac{z}{(m-\tfrac{1}{2}+(n-\tfrac{1}{2})\tau)\pi}% \right),}}
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    DLMF:20.5.E16
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