DLMF:20.2.E13 (Q6753)

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DLMF:20.2.E13
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    θ 3 ( z | τ ) = θ 4 ( z + 1 2 π | τ ) = M θ 2 ( z + 1 2 π τ | τ ) = M θ 1 ( z + 1 2 π + 1 2 π τ | τ ) , Jacobi-theta-tau 3 𝑧 𝜏 Jacobi-theta-tau 4 𝑧 1 2 𝜋 𝜏 𝑀 Jacobi-theta-tau 2 𝑧 1 2 𝜋 𝜏 𝜏 𝑀 Jacobi-theta-tau 1 𝑧 1 2 𝜋 1 2 𝜋 𝜏 𝜏 {\displaystyle{\displaystyle\theta_{3}\left(z\middle|\tau\right)=\theta_{4}% \left(z+\tfrac{1}{2}\pi\middle|\tau\right)=M\theta_{2}\left(z+\tfrac{1}{2}\pi% \tau\middle|\tau\right)=M\theta_{1}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau% \middle|\tau\right),}}
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    DLMF:20.2.E13
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