DLMF:21.6.E8 (Q6896): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11970 / rank
 
Normal rank
Property / Symbols used: Q11970 / qualifier
 
Defining formula:

𝜸 𝜸 {\displaystyle{\displaystyle\boldsymbol{{\gamma}}}}

\boldsymbol{{\gamma}}
Property / Symbols used: Q11970 / qualifier
 
xml-id: C21.S6.XMD5.m1dec

Latest revision as of 14:52, 2 January 2020

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DLMF:21.6.E8
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    Statements

    θ [ 𝜶 𝜸 ] ( 𝐳 1 | 𝛀 ) θ [ 𝜷 𝜹 ] ( 𝐳 2 | 𝛀 ) = 𝝂 g / ( 2 g ) θ [ 1 2 [ 𝜶 + 𝜷 + 𝝂 ] 𝜸 + 𝜹 ] ( 𝐳 1 + 𝐳 2 | 2 𝛀 ) θ [ 1 2 [ 𝜶 - 𝜷 + 𝝂 ] 𝜸 - 𝜹 ] ( 𝐳 1 - 𝐳 2 | 2 𝛀 ) . Riemann-theta-characterstics 𝜶 𝜸 subscript 𝐳 1 𝛀 Riemann-theta-characterstics 𝜷 𝜹 subscript 𝐳 2 𝛀 subscript 𝝂 𝑔 2 𝑔 Riemann-theta-characterstics 1 2 delimited-[] 𝜶 𝜷 𝝂 𝜸 𝜹 subscript 𝐳 1 subscript 𝐳 2 2 𝛀 Riemann-theta-characterstics 1 2 delimited-[] 𝜶 𝜷 𝝂 𝜸 𝜹 subscript 𝐳 1 subscript 𝐳 2 2 𝛀 {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}% }}{\boldsymbol{{\gamma}}}\left(\mathbf{z}_{1}\middle|\boldsymbol{{\Omega}}% \right)\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\beta}}}{\boldsymbol{{\delta% }}}\left(\mathbf{z}_{2}\middle|\boldsymbol{{\Omega}}\right)=\sum_{\boldsymbol{% {\nu}}\in{\mathbb{Z}^{g}}/\left(2{\mathbb{Z}^{g}}\right)}\theta\genfrac{[}{]}{% 0.0pt}{}{\frac{1}{2}[\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}+\boldsymbol{{% \nu}}]}{\boldsymbol{{\gamma}}+\boldsymbol{{\delta}}}\left(\mathbf{z}_{1}+% \mathbf{z}_{2}\middle|2\boldsymbol{{\Omega}}\right)\*\theta\genfrac{[}{]}{0.0% pt}{}{\frac{1}{2}[\boldsymbol{{\alpha}}-\boldsymbol{{\beta}}+\boldsymbol{{\nu}% }]}{\boldsymbol{{\gamma}}-\boldsymbol{{\delta}}}\left(\mathbf{z}_{1}-\mathbf{z% }_{2}\middle|2\boldsymbol{{\Omega}}\right).}}
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    DLMF:21.6.E8
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    θ [ 𝜶 𝜷 ] ( | missing ) Riemann-theta-characterstics 𝜶 𝜷 missing {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\NVar{\boldsymbol{{% \alpha}}}}{\NVar{\boldsymbol{{\beta}}}}\left(\middle|missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    C21.S2.E5.m2abdec
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    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2addec
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    {\displaystyle{\displaystyle\mathbb{Z}}}
    introduction.Sx4.p2.t1.r20.m2addec
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    g 𝑔 {\displaystyle{\displaystyle g}}
    C21.S1.XMD1.m1edec
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    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    C21.S1.XMD3.m1ddec
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    𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
    C21.S1.XMD4.m1bdec
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    𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
    C21.S1.XMD5.m1bdec
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    𝜹 𝜹 {\displaystyle{\displaystyle\boldsymbol{{\delta}}}}
    C21.S6.XMD4.m1dec
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    𝜸 𝜸 {\displaystyle{\displaystyle\boldsymbol{{\gamma}}}}
    C21.S6.XMD5.m1dec
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