DLMF:21.7.E10 (Q6908): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11977 / rank
 
Normal rank
Property / Symbols used: Q11977 / qualifier
 
Defining formula:

𝝎 𝝎 {\displaystyle{\displaystyle\boldsymbol{{\omega}}}}

\boldsymbol{{\omega}}
Property / Symbols used: Q11977 / qualifier
 
xml-id: C21.S7.XMD9.m1adec

Latest revision as of 14:53, 2 January 2020

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DLMF:21.7.E10
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    Statements

    Defining formula
    θ ⁡ ( 𝐳 + ∫ P 1 P 3 𝝎 | 𝛀 ) ⁢ θ ⁡ ( 𝐳 + ∫ P 2 P 4 𝝎 | 𝛀 ) ⁢ E ⁢ ( P 3 , P 2 ) ⁢ E ⁢ ( P 1 , P 4 ) + θ ⁡ ( 𝐳 + ∫ P 2 P 3 𝝎 | 𝛀 ) ⁢ θ ⁡ ( 𝐳 + ∫ P 1 P 4 𝝎 | 𝛀 ) ⁢ E ⁢ ( P 3 , P 1 ) ⁢ E ⁢ ( P 4 , P 2 ) = θ ⁡ ( 𝐳 | 𝛀 ) ⁢ θ ⁡ ( 𝐳 + ∫ P 1 P 3 𝝎 + ∫ P 2 P 4 𝝎 | 𝛀 ) ⁢ E ⁢ ( P 1 , P 2 ) ⁢ E ⁢ ( P 3 , P 4 ) , Riemann-theta 𝐳 superscript subscript subscript 𝑃 1 subscript 𝑃 3 𝝎 𝛀 Riemann-theta 𝐳 superscript subscript subscript 𝑃 2 subscript 𝑃 4 𝝎 𝛀 𝐸 subscript 𝑃 3 subscript 𝑃 2 𝐸 subscript 𝑃 1 subscript 𝑃 4 Riemann-theta 𝐳 superscript subscript subscript 𝑃 2 subscript 𝑃 3 𝝎 𝛀 Riemann-theta 𝐳 superscript subscript subscript 𝑃 1 subscript 𝑃 4 𝝎 𝛀 𝐸 subscript 𝑃 3 subscript 𝑃 1 𝐸 subscript 𝑃 4 subscript 𝑃 2 Riemann-theta 𝐳 𝛀 Riemann-theta 𝐳 superscript subscript subscript 𝑃 1 subscript 𝑃 3 𝝎 superscript subscript subscript 𝑃 2 subscript 𝑃 4 𝝎 𝛀 𝐸 subscript 𝑃 1 subscript 𝑃 2 𝐸 subscript 𝑃 3 subscript 𝑃 4 {\displaystyle{\displaystyle\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{3}}% \boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z% }+\int_{P_{2}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right% )E(P_{3},P_{2})E(P_{1},P_{4})+\theta\left(\mathbf{z}+\int_{P_{2}}^{P_{3}}% \boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z% }+\int_{P_{1}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right% )E(P_{3},P_{1})E(P_{4},P_{2})=\theta\left(\mathbf{z}\middle|\boldsymbol{{% \Omega}}\right)\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{3}}\boldsymbol{{\omega}% }+\int_{P_{2}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right% )E(P_{1},P_{2})E(P_{3},P_{4}),}}
    0 references
    DLMF id
    DLMF:21.7.E10
    0 references
    Symbols used
    Riemann theta function
    Defining formula
    θ ⁡ ( 𝐳 | 𝛀 ) Riemann-theta 𝐳 𝛀 {\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{% \boldsymbol{{\Omega}}}\right)}}
    xml-id
    C21.S2.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6aadec
    0 references
    Q11960
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1cdec
    0 references
    prime form (locally)
    Defining formula
    E ⁢ ( P 1 , P 2 ) 𝐸 subscript 𝑃 1 subscript 𝑃 2 {\displaystyle{\displaystyle E(P_{1},P_{2})}}
    xml-id
    C21.S7.XMD7.m1adec
    0 references
    Q11976
    Defining formula
    P 1 , P 2 subscript 𝑃 1 subscript 𝑃 2 {\displaystyle{\displaystyle P_{1},P_{2}}}
    xml-id
    C21.S7.XMD8.m1adec
    0 references
    Q11977
    Defining formula
    𝝎 𝝎 {\displaystyle{\displaystyle\boldsymbol{{\omega}}}}
    xml-id
    C21.S7.XMD9.m1adec
    0 references
     
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