DLMF:21.2.E1 (Q6857): Difference between revisions

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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.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10818 / rank
 
Normal rank
Property / Symbols used: Q10818 / qualifier
 
Defining formula:

ℤ {\displaystyle{\displaystyle\mathbb{Z}}}

\Integers
Property / Symbols used: Q10818 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r20.m2adec
Property / Symbols used
 
Property / Symbols used: Q11959 / rank
 
Normal rank
Property / Symbols used: Q11959 / qualifier
 
Defining formula:

g 𝑔 {\displaystyle{\displaystyle g}}

g
Property / Symbols used: Q11959 / qualifier
 
xml-id: C21.S1.XMD1.m1dec
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.m1dec

Latest revision as of 14:46, 2 January 2020

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English
DLMF:21.2.E1
No description defined

    Statements

    Defining formula
    θ ⁡ ( 𝐳 | 𝛀 ) = ∑ 𝐧 ∈ ℤ g e 2 ⁢ π ⁢ i ⁢ ( 1 2 ⁢ 𝐧 ⋅ 𝛀 ⋅ 𝐧 + 𝐧 ⋅ 𝐳 ) . Riemann-theta 𝐳 𝛀 subscript 𝐧 𝑔 superscript 𝑒 2 𝜋 𝑖 ⋅ 1 2 𝐧 𝛀 𝐧 ⋅ 𝐧 𝐳 {\displaystyle{\displaystyle\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}% }\right)=\sum_{\mathbf{n}\in{\mathbb{Z}^{g}}}e^{2\pi i\left(\frac{1}{2}\mathbf% {n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}% .}}
    0 references
    DLMF id
    DLMF:21.2.E1
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2adec
    0 references
    Q11959
    Defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C21.S1.XMD1.m1dec
    0 references
    Q11960
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1dec
    0 references
     
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