DLMF:20.8.E1 (Q6830)

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DLMF:20.8.E1
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    θ 2 ( 0 , q ) θ 3 ( z , q ) θ 4 ( z , q ) θ 2 ( z , q ) = 2 n = - ( - 1 ) n q n 2 e i 2 n z q - n e - i z + q n e i z . Jacobi-theta 2 0 𝑞 Jacobi-theta 3 𝑧 𝑞 Jacobi-theta 4 𝑧 𝑞 Jacobi-theta 2 𝑧 𝑞 2 superscript subscript 𝑛 superscript 1 𝑛 superscript 𝑞 superscript 𝑛 2 superscript 𝑒 𝑖 2 𝑛 𝑧 superscript 𝑞 𝑛 superscript 𝑒 𝑖 𝑧 superscript 𝑞 𝑛 superscript 𝑒 𝑖 𝑧 {\displaystyle{\displaystyle\frac{\theta_{2}\left(0,q\right)\theta_{3}\left(z,% q\right)\theta_{4}\left(z,q\right)}{\theta_{2}\left(z,q\right)}=2\sum_{n=-% \infty}^{\infty}\frac{(-1)^{n}q^{n^{2}}e^{i2nz}}{q^{-n}e^{-iz}+q^{n}e^{iz}}.}}
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    DLMF:20.8.E1
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