DLMF:21.3.E6 (Q6874): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Riemann theta function with characteristics / rank
 
Normal rank
Property / Symbols used: Riemann theta function with characteristics / qualifier
 
Defining formula:

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}}}

\Riemannthetachar{\NVar{\boldsymbol{{\alpha}}}}{\NVar{\boldsymbol{{\beta}}}}@{% \NVar{\mathbf{z}}}{\NVar{\boldsymbol{{\Omega}}}}
Property / Symbols used: Riemann theta function with characteristics / qualifier
 
xml-id: C21.S2.E5.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11960 / rank
 
Normal rank
Property / Symbols used: Q11960 / qualifier
 
Defining formula:

𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}

\boldsymbol{{\Omega}}
Property / Symbols used: Q11960 / qualifier
 
xml-id: C21.S1.XMD3.m1edec
Property / Symbols used
 
Property / Symbols used: Q11961 / rank
 
Normal rank
Property / Symbols used: Q11961 / qualifier
 
Defining formula:

𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}

\boldsymbol{{\alpha}}
Property / Symbols used: Q11961 / qualifier
 
xml-id: C21.S1.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11962 / rank
 
Normal rank
Property / Symbols used: Q11962 / qualifier
 
Defining formula:

𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}

\boldsymbol{{\beta}}
Property / Symbols used: Q11962 / qualifier
 
xml-id: C21.S1.XMD5.m1bdec

Latest revision as of 14:48, 2 January 2020

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DLMF:21.3.E6
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    Statements

    θ [ 𝜶 𝜷 ] ( - 𝐳 | 𝛀 ) = ( - 1 ) 4 𝜶 𝜷 θ [ 𝜶 𝜷 ] ( 𝐳 | 𝛀 ) . Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 superscript 1 4 𝜶 𝜷 Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}% }}{\boldsymbol{{\beta}}}\left(-\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)=% (-1)^{4\boldsymbol{{\alpha}}\cdot\boldsymbol{{\beta}}}\theta\genfrac{[}{]}{0.0% pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(\mathbf{z}\middle|% \boldsymbol{{\Omega}}\right).}}
    0 references
    DLMF:21.3.E6
    0 references
    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
    0 references
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    C21.S1.XMD3.m1edec
    0 references
    𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
    C21.S1.XMD4.m1bdec
    0 references
    𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
    C21.S1.XMD5.m1bdec
    0 references