DLMF:21.7.E7 (Q6905)

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DLMF:21.7.E7
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    Statements

    Defining formula
    ( ∂ ∂ ⁡ z 1 ⁡ θ ⁢ [ 𝜶 𝜷 ] ⁡ ( 𝐳 | 𝛀 ) | 𝐳 = 𝟎 , … , ∂ ∂ ⁡ z g ⁡ θ ⁢ [ 𝜶 𝜷 ] ⁡ ( 𝐳 | 𝛀 ) | 𝐳 = 𝟎 ) ≠ 𝟎 . evaluated-at partial-derivative subscript 𝑧 1 Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 𝐳 0 … evaluated-at partial-derivative subscript 𝑧 𝑔 Riemann-theta-characterstics 𝜶 𝜷 𝐳 𝛀 𝐳 0 0 {\displaystyle{\displaystyle\left(\frac{\partial}{\partial z_{1}}\theta% \genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(% \mathbf{z}\middle|\boldsymbol{{\Omega}}\right)\Big{|}_{\mathbf{z}=\boldsymbol{% {0}}},\dots,\frac{\partial}{\partial z_{g}}\theta\genfrac{[}{]}{0.0pt}{}{% \boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(\mathbf{z}\middle|% \boldsymbol{{\Omega}}\right)\Big{|}_{\mathbf{z}=\boldsymbol{{0}}}\right)\neq% \boldsymbol{{0}}.}}
    0 references
    DLMF id
    DLMF:21.7.E7
    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.m2adec
    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.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
     
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