DLMF:21.7.E17 (Q6916): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
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.m1ddec
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.m1cdec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11981 / rank
 
Normal rank
Property / Symbols used: Q11981 / qualifier
 
Defining formula:

P j subscript 𝑃 𝑗 {\displaystyle{\displaystyle P_{j}}}

P_{j}
Property / Symbols used: Q11981 / qualifier
 
xml-id: C21.S7.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11980 / rank
 
Normal rank
Property / Symbols used: Q11980 / qualifier
 
Defining formula:

U 𝑈 {\displaystyle{\displaystyle U}}

U
Property / Symbols used: Q11980 / qualifier
 
xml-id: C21.S7.XMD13.m1adec

Latest revision as of 14:54, 2 January 2020

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English
DLMF:21.7.E17
No description defined

    Statements

    Defining formula
    ∑ 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).}}
    0 references
    DLMF id
    DLMF:21.7.E17
    0 references
    Symbols used
    Riemann theta function with characteristics
    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}}}
    xml-id
    C21.S2.E5.m2acdec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    Q11960
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1ddec
    0 references
    Q11961
    Defining formula
    𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
    xml-id
    C21.S1.XMD4.m1cdec
    0 references
    Q11962
    Defining formula
    𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
    xml-id
    C21.S1.XMD5.m1cdec
    0 references
    Q11981
    Defining formula
    P j subscript 𝑃 𝑗 {\displaystyle{\displaystyle P_{j}}}
    xml-id
    C21.S7.XMD10.m1dec
    0 references
    Q11980
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C21.S7.XMD13.m1adec
    0 references
     
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