DLMF:21.7.E8 (Q6906)

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DLMF:21.7.E8
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    Statements

    Defining formula
    ζ = ∑ j = 1 g ω j ⁢ ∂ ∂ ⁡ z j ⁡ θ ⁢ [ 𝜶 𝜷 ] ⁡ ( 𝐳 | 𝛀 ) | 𝐳 = 𝟎 . 𝜁 evaluated-at superscript subscript 𝑗 1 𝑔 subscript 𝜔 𝑗 partial-derivative subscript 𝑧 𝑗 Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 𝐳 0 {\displaystyle{\displaystyle\zeta=\sum_{j=1}^{g}\omega_{j}\frac{\partial}{% \partial z_{j}}\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{% \boldsymbol{{\beta}}}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)\Big{% |}_{\mathbf{z}=\boldsymbol{{0}}}.}}
    0 references
    DLMF id
    DLMF:21.7.E8
    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.m2aadec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4aadec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q11959
    Defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C21.S1.XMD1.m1ddec
    0 references
    Q11960
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1adec
    0 references
     
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