DLMF:21.6.E7 (Q6895): 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
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10818 / rank
 
Normal rank
Property / Symbols used: Q10818 / qualifier
 
test:

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

\Integers
Property / Symbols used: Q10818 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r20.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11959 / rank
 
Normal rank
Property / Symbols used: Q11959 / qualifier
 
test:

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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11960 / rank
 
Normal rank
Property / Symbols used: Q11960 / qualifier
 
test:

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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11961 / rank
 
Normal rank
Property / Symbols used: Q11961 / qualifier
 
test:

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

\boldsymbol{{\alpha}}
Property / Symbols used: Q11961 / qualifier
 
xml-id: C21.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11962 / rank
 
Normal rank
Property / Symbols used: Q11962 / qualifier
 
test:

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

\boldsymbol{{\beta}}
Property / Symbols used: Q11962 / qualifier
 
xml-id: C21.S1.XMD5.m1adec

Latest revision as of 13:51, 2 January 2020

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English
DLMF:21.6.E7
No description defined

    Statements

    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}+\mathbf{c}_{2}+\mathbf{c}_{3}+\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}+\mathbf{d}_{2}+\mathbf{d}_{3}+\mathbf{d}_{4}]}@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}+\mathbf{c}_{2}-\mathbf{c}_{3}-\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}+\mathbf{d}_{2}-\mathbf{d}_{3}-\mathbf{d}_{4}]}@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\*\Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}-\mathbf{c}_{2}+\mathbf{c}_{3}-\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}-\mathbf{d}_{2}+\mathbf{d}_{3}-\mathbf{d}_{4}]}@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}-\mathbf{c}_{2}-\mathbf{c}_{3}+\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}-\mathbf{d}_{2}-\mathbf{d}_{3}+\mathbf{d}_{4}]}@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\\ =\frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{-2\pi i\boldsymbol{{\beta}}\cdot[\mathbf{c}_{1}+\mathbf{c}_{2}+\mathbf{c}_{3}+\mathbf{c}_{4}]}\*\Riemannthetachar{\mathbf{c}_{1}+\boldsymbol{{\alpha}}}{\mathbf{d}_{1}+\boldsymbol{{\beta}}}@{\mathbf{x}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\mathbf{c}_{2}+\boldsymbol{{\alpha}}}{\mathbf{d}_{2}+\boldsymbol{{\beta}}}@{\mathbf{y}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\mathbf{c}_{3}+\boldsymbol{{\alpha}}}{\mathbf{d}_{3}+\boldsymbol{{\beta}}}@{\mathbf{u}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\mathbf{c}_{4}+\boldsymbol{{\alpha}}}{\mathbf{d}_{4}+\boldsymbol{{\beta}}}@{\mathbf{v}}{\boldsymbol{{\Omega}}}.}
    0 references
    DLMF id
    DLMF:21.6.E7
    0 references
    Symbols used
    Riemann theta function with characteristics
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannthetachar{\NVar{\boldsymbol{{\alpha}}}}{\NVar{\boldsymbol{{\beta}}}}@{% \NVar{\mathbf{z}}}{\NVar{\boldsymbol{{\Omega}}}}}
    xml-id
    C21.S2.E5.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10784
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \in}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
    0 references
    base of natural logarithm
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10818
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Integers}
    xml-id
    introduction.Sx4.p2.t1.r20.m2acdec
    0 references
    Q11959
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g}
    xml-id
    C21.S1.XMD1.m1ddec
    0 references
    Q11960
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{\Omega}}}
    xml-id
    C21.S1.XMD3.m1cdec
    0 references
    Q11961
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{\alpha}}}
    xml-id
    C21.S1.XMD4.m1adec
    0 references
    Q11962
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{\beta}}}
    xml-id
    C21.S1.XMD5.m1adec
    0 references
     
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