DLMF:21.3.E3 (Q6871): 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
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 13:48, 2 January 2020

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DLMF:21.3.E3
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    Statements

    test
    θ ⁡ ( 𝐳 + 𝐦 1 + 𝛀 ⁢ 𝐦 2 | 𝛀 ) = e - 2 ⁢ π ⁢ i ⁢ ( 1 2 ⁢ 𝐦 2 ⋅ 𝛀 ⋅ 𝐦 2 + 𝐦 2 ⋅ 𝐳 ) ⁢ θ ⁡ ( 𝐳 | 𝛀 ) , Riemann-theta 𝐳 subscript 𝐦 1 𝛀 subscript 𝐦 2 𝛀 superscript 𝑒 2 𝜋 𝑖 ⋅ 1 2 subscript 𝐦 2 𝛀 subscript 𝐦 2 ⋅ subscript 𝐦 2 𝐳 Riemann-theta 𝐳 𝛀 {\displaystyle{\displaystyle\theta\left(\mathbf{z}+\mathbf{m}_{1}+\boldsymbol{% {\Omega}}\mathbf{m}_{2}\middle|\boldsymbol{{\Omega}}\right)=e^{-2\pi i\left(% \frac{1}{2}\mathbf{m}_{2}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{m}_{2}+\mathbf% {m}_{2}\cdot\mathbf{z}\right)}\theta\left(\mathbf{z}\middle|\boldsymbol{{% \Omega}}\right),}}
    0 references
    DLMF id
    DLMF:21.3.E3
    0 references
    Symbols used
    Riemann theta function
    test
    θ ⁡ ( 𝐳 | 𝛀 ) Riemann-theta 𝐳 𝛀 {\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{% \boldsymbol{{\Omega}}}\right)}}
    xml-id
    C21.S2.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
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