DLMF:21.6.E3 (Q6891): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \in}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11967 / rank
 
Normal rank
Property / Symbols used: Q11967 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \trace\NVar{\mathbf{A}}}

\trace\NVar{\mathbf{A}}
Property / Symbols used: Q11967 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r7.m3adec
Property / Symbols used
 
Property / Symbols used: Q11959 / rank
 
Normal rank
Property / Symbols used: Q11959 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g}

g
Property / Symbols used: Q11959 / qualifier
 
xml-id: C21.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11966 / rank
 
Normal rank
Property / Symbols used: Q11966 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h}

h
Property / Symbols used: Q11966 / qualifier
 
xml-id: C21.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11960 / rank
 
Normal rank
Property / Symbols used: Q11960 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{\Omega}}}

\boldsymbol{{\Omega}}
Property / Symbols used: Q11960 / qualifier
 
xml-id: C21.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11968 / rank
 
Normal rank
Property / Symbols used: Q11968 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T_{jk}}

T_{jk}
Property / Symbols used: Q11968 / qualifier
 
xml-id: C21.S6.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: set of matrices (locally) / rank
 
Normal rank
Property / Symbols used: set of matrices (locally) / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{K}}

\mathcal{K}
Property / Symbols used: set of matrices (locally) / qualifier
 
xml-id: C21.S6.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: number of elements (locally) / rank
 
Normal rank
Property / Symbols used: number of elements (locally) / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{D}}

\mathcal{D}
Property / Symbols used: number of elements (locally) / qualifier
 
xml-id: C21.S6.XMD3.m1adec

Latest revision as of 14:50, 2 January 2020

No description defined
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English
DLMF:21.6.E3
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \prod_{j=1}^{h}\Riemanntheta@{\sum_{k=1}^{h}T_{jk}\mathbf{z}_{k}}{\boldsymbol{{\Omega}}}=\frac{1}{\mathcal{D}^{g}}\sum_{\mathbf{A}\in\mathcal{K}}\sum_{\mathbf{B}\in\mathcal{K}}e^{2\pi i\trace\left[\frac{1}{2}\transpose{\mathbf{A}}\boldsymbol{{\Omega}}\mathbf{A}+\transpose{\mathbf{A}}[\mathbf{Z}+\mathbf{B}]\right]}\*\prod_{j=1}^{h}\Riemanntheta@{\mathbf{z}_{j}+\boldsymbol{{\Omega}}\mathbf{a}_{j}+\mathbf{b}_{j}}{\boldsymbol{{\Omega}}},}
    0 references
    DLMF id
    DLMF:21.6.E3
    0 references
    Symbols used
    Riemann theta function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{\NVar{\mathbf{z}}}{\NVar{\boldsymbol{{\Omega}}}}}
    xml-id
    C21.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10784
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \in}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    base of natural logarithm
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11967
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \trace\NVar{\mathbf{A}}}
    xml-id
    introduction.Sx4.p2.t1.r7.m3adec
    0 references
    Q11959
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g}
    xml-id
    C21.S1.XMD1.m1adec
    0 references
    Q11966
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h}
    xml-id
    C21.S1.XMD2.m1bdec
    0 references
    Q11960
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{\Omega}}}
    xml-id
    C21.S1.XMD3.m1dec
    0 references
    Q11968
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T_{jk}}
    xml-id
    C21.S6.XMD1.m1dec
    0 references
    set of matrices (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{K}}
    xml-id
    C21.S6.XMD2.m1adec
    0 references
    number of elements (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{D}}
    xml-id
    C21.S6.XMD3.m1adec
    0 references
     
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