DLMF:20.5.E7 (Q6774)

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DLMF:20.5.E7
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    θ 3 ( z | τ ) = θ 3 ( 0 | τ ) n = 1 cos ( ( n - 1 2 ) π τ + z ) cos ( ( n - 1 2 ) π τ - z ) cos 2 ( ( n - 1 2 ) π τ ) , Jacobi-theta-tau 3 𝑧 𝜏 Jacobi-theta-tau 3 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_{3}\left(z\middle|\tau\right)=\theta_{3}% \left(0\middle|\tau\right)\prod_{n=1}^{\infty}\frac{\cos\left((n-\tfrac{1}{2})% \pi\tau+z\right)\cos\left((n-\tfrac{1}{2})\pi\tau-z\right)}{{\cos^{2}}\left((n% -\tfrac{1}{2})\pi\tau\right)},}}
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    DLMF:20.5.E7
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