DLMF:21.2.E9 (Q6865): Difference between revisions

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Changed an Item: Add constraint
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.m2acdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2agdec

Latest revision as of 14:47, 2 January 2020

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DLMF:21.2.E9
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    Statements

    θ 1 ( π z | Ω ) = - θ [ 1 2 1 2 ] ( z | Ω ) , Jacobi-theta-tau 1 𝜋 𝑧 Ω Riemann-theta-characterstics 1 2 1 2 𝑧 Ω {\displaystyle{\displaystyle\theta_{1}\left(\pi z\middle|\Omega\right)=-\theta% \genfrac{[}{]}{0.0pt}{}{\frac{1}{2}}{\frac{1}{2}}\left(z\middle|\Omega\right),}}
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    DLMF:21.2.E9
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    θ j ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    C20.S2.SS1.m1aadec
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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.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2agdec
    0 references