DLMF:21.7.E17 (Q6916)

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DLMF:21.7.E17
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    P j U k = 1 4 θ [ 𝜶 k + 𝜼 1 ( P j ) 𝜷 k + 𝜼 2 ( P j ) ] ( 𝐳 k | 𝛀 ) = P j U c k = 1 4 θ [ 𝜶 k + 𝜼 1 ( P j ) 𝜷 k + 𝜼 2 ( P j ) ] ( 𝐳 k | 𝛀 ) . subscript subscript 𝑃 𝑗 𝑈 superscript subscript product 𝑘 1 4 Riemann-theta-characterstics subscript 𝜶 𝑘 superscript 𝜼 1 subscript 𝑃 𝑗 subscript 𝜷 𝑘 superscript 𝜼 2 subscript 𝑃 𝑗 subscript 𝐳 𝑘 𝛀 subscript subscript 𝑃 𝑗 superscript 𝑈 𝑐 superscript subscript product 𝑘 1 4 Riemann-theta-characterstics subscript 𝜶 𝑘 superscript 𝜼 1 subscript 𝑃 𝑗 subscript 𝜷 𝑘 superscript 𝜼 2 subscript 𝑃 𝑗 subscript 𝐳 𝑘 𝛀 {\displaystyle{\displaystyle\sum_{P_{j}\in U}\prod_{k=1}^{4}\theta\genfrac{[}{% ]}{0.0pt}{}{\boldsymbol{{\alpha}}_{k}+\boldsymbol{{\eta}}^{1}(P_{j})}{% \boldsymbol{{\beta}}_{k}+\boldsymbol{{\eta}}^{2}(P_{j})}\left(\mathbf{z}_{k}% \middle|\boldsymbol{{\Omega}}\right)=\sum_{P_{j}\in U^{c}}\prod_{k=1}^{4}% \theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}_{k}+\boldsymbol{{\eta}}^{1% }(P_{j})}{\boldsymbol{{\beta}}_{k}+\boldsymbol{{\eta}}^{2}(P_{j})}\left(% \mathbf{z}_{k}\middle|\boldsymbol{{\Omega}}\right).}}
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    DLMF:21.7.E17
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