DLMF:21.7.E10 (Q6908)

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DLMF:21.7.E10
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    θ ( 𝐳 + P 1 P 3 𝝎 | 𝛀 ) θ ( 𝐳 + P 2 P 4 𝝎 | 𝛀 ) E ( P 3 , P 2 ) E ( P 1 , P 4 ) + θ ( 𝐳 + P 2 P 3 𝝎 | 𝛀 ) θ ( 𝐳 + P 1 P 4 𝝎 | 𝛀 ) E ( P 3 , P 1 ) E ( P 4 , P 2 ) = θ ( 𝐳 | 𝛀 ) θ ( 𝐳 + P 1 P 3 𝝎 + P 2 P 4 𝝎 | 𝛀 ) E ( P 1 , P 2 ) E ( P 3 , P 4 ) , Riemann-theta 𝐳 superscript subscript subscript 𝑃 1 subscript 𝑃 3 𝝎 𝛀 Riemann-theta 𝐳 superscript subscript subscript 𝑃 2 subscript 𝑃 4 𝝎 𝛀 𝐸 subscript 𝑃 3 subscript 𝑃 2 𝐸 subscript 𝑃 1 subscript 𝑃 4 Riemann-theta 𝐳 superscript subscript subscript 𝑃 2 subscript 𝑃 3 𝝎 𝛀 Riemann-theta 𝐳 superscript subscript subscript 𝑃 1 subscript 𝑃 4 𝝎 𝛀 𝐸 subscript 𝑃 3 subscript 𝑃 1 𝐸 subscript 𝑃 4 subscript 𝑃 2 Riemann-theta 𝐳 𝛀 Riemann-theta 𝐳 superscript subscript subscript 𝑃 1 subscript 𝑃 3 𝝎 superscript subscript subscript 𝑃 2 subscript 𝑃 4 𝝎 𝛀 𝐸 subscript 𝑃 1 subscript 𝑃 2 𝐸 subscript 𝑃 3 subscript 𝑃 4 {\displaystyle{\displaystyle\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{3}}% \boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z% }+\int_{P_{2}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right% )E(P_{3},P_{2})E(P_{1},P_{4})+\theta\left(\mathbf{z}+\int_{P_{2}}^{P_{3}}% \boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z% }+\int_{P_{1}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right% )E(P_{3},P_{1})E(P_{4},P_{2})=\theta\left(\mathbf{z}\middle|\boldsymbol{{% \Omega}}\right)\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{3}}\boldsymbol{{\omega}% }+\int_{P_{2}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right% )E(P_{1},P_{2})E(P_{3},P_{4}),}}
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    DLMF:21.7.E10
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