DLMF:21.2.E1 (Q6857)

From DRMF
Revision as of 14:46, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6857&oldid=50666"