DLMF:20.6.E4 (Q6788)

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DLMF:20.6.E4
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    Defining formula
    θ 3 ⁡ ( π ⁢ z | τ ) = θ 3 ⁡ ( 0 | τ ) ⁢ exp ⁡ ( - ∑ j = 1 ∞ 1 2 ⁢ j ⁢ β 2 ⁢ j ⁢ ( τ ) ⁢ z 2 ⁢ j ) , Jacobi-theta-tau 3 𝜋 𝑧 𝜏 Jacobi-theta-tau 3 0 𝜏 superscript subscript 𝑗 1 1 2 𝑗 subscript 𝛽 2 𝑗 𝜏 superscript 𝑧 2 𝑗 {\displaystyle{\displaystyle\theta_{3}\left(\pi z\middle|\tau\right)=\theta_{3% }\left(0\middle|\tau\right)\exp\left(-\sum_{j=1}^{\infty}\frac{1}{2j}\beta_{2j% }(\tau)z^{2j}\right),}}
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    DLMF id
    DLMF:20.6.E4
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