DLMF:21.3.E4 (Q6872): Difference between revisions

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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.m2aadec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec
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.m1cdec
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.m1dec
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.m1dec

Latest revision as of 14:48, 2 January 2020

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English
DLMF:21.3.E4
No description defined

    Statements

    Defining formula
    θ ⁢ [ 𝜶 + 𝐦 1 𝜷 + 𝐦 2 ] ⁡ ( 𝐳 | 𝛀 ) = e 2 ⁢ π ⁢ i ⁢ 𝜶 ⋅ 𝐦 2 ⁢ θ ⁢ [ 𝜶 𝜷 ] ⁡ ( 𝐳 | 𝛀 ) . Riemann-theta-characterstics 𝜶 subscript 𝐦 1 𝜷 subscript 𝐦 2 𝐳 𝛀 superscript 𝑒 ⋅ 2 𝜋 𝑖 𝜶 subscript 𝐦 2 Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 {\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}% }+\mathbf{m}_{1}}{\boldsymbol{{\beta}}+\mathbf{m}_{2}}\left(\mathbf{z}\middle|% \boldsymbol{{\Omega}}\right)=e^{2\pi i\boldsymbol{{\alpha}}\cdot\mathbf{m}_{2}% }\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}% \left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right).}}
    0 references
    DLMF id
    DLMF:21.3.E4
    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q11960
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1cdec
    0 references
    Q11961
    Defining formula
    𝜶 𝜶 {\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}
    xml-id
    C21.S1.XMD4.m1dec
    0 references
    Q11962
    Defining formula
    𝜷 𝜷 {\displaystyle{\displaystyle\boldsymbol{{\beta}}}}
    xml-id
    C21.S1.XMD5.m1dec
    0 references
     
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