DLMF:20.5.E8 (Q6775)

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DLMF:20.5.E8
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    θ 4 ( z | τ ) = θ 4 ( 0 | τ ) n = 1 sin ( ( n - 1 2 ) π τ + z ) sin ( ( n - 1 2 ) π τ - z ) sin 2 ( ( n - 1 2 ) π τ ) . Jacobi-theta-tau 4 𝑧 𝜏 Jacobi-theta-tau 4 0 𝜏 superscript subscript product 𝑛 1 𝑛 1 2 𝜋 𝜏 𝑧 𝑛 1 2 𝜋 𝜏 𝑧 2 𝑛 1 2 𝜋 𝜏 {\displaystyle{\displaystyle\theta_{4}\left(z\middle|\tau\right)=\theta_{4}% \left(0\middle|\tau\right)\prod_{n=1}^{\infty}\frac{\sin\left((n-\tfrac{1}{2})% \pi\tau+z\right)\sin\left((n-\tfrac{1}{2})\pi\tau-z\right)}{{\sin^{2}}\left((n% -\tfrac{1}{2})\pi\tau\right)}.}}
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    DLMF:20.5.E8
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