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DLMF:21.2.E6 - MaRDI portal
Statements
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[
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]
(
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=
e
2
π
i
(
1
2
𝜶
⋅
𝛀
⋅
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+
𝜶
⋅
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𝐳
+
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]
)
θ
(
𝐳
+
𝛀
𝜶
+
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|
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)
,
Riemann-theta-characterstics
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𝐳
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superscript
𝑒
2
𝜋
𝑖
⋅
1
2
𝜶
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⋅
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delimited-[]
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Riemann-theta
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𝛀
𝜶
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𝛀
{\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}%
}}{\boldsymbol{{\beta}}}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)=e%
^{2\pi i\left(\frac{1}{2}\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot%
\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{z}+\boldsymbol{{\beta%
}}]\right)}\theta\left(\mathbf{z}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+%
\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right),}}
θ
(
𝐳
|
𝛀
)
Riemann-theta
𝐳
𝛀
{\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{%
\boldsymbol{{\Omega}}}\right)}}
θ
[
𝜶
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]
(
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missing
)
Riemann-theta-characterstics
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missing
{\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\NVar{\boldsymbol{{%
\alpha}}}}{\NVar{\boldsymbol{{\beta}}}}\left(\middle|missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
𝛀
𝛀
{\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
𝜶
𝜶
{\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
𝜷
𝜷
{\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
Identifiers