DLMF:5.20.E3 (Q2208): Difference between revisions

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‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec
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: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
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: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

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

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
Defining formula:

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

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2adec
Property / Symbols used
 
Property / Symbols used: Q11292 / rank
 
Normal rank
Property / Symbols used: Q11292 / qualifier
 
Defining formula:

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

j
Property / Symbols used: Q11292 / qualifier
 
xml-id: C5.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11274 / rank
 
Normal rank
Property / Symbols used: Q11274 / qualifier
 
Defining formula:

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

n
Property / Symbols used: Q11274 / qualifier
 
xml-id: C5.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11281 / rank
 
Normal rank
Property / Symbols used: Q11281 / qualifier
 
Defining formula:

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

x
Property / Symbols used: Q11281 / qualifier
 
xml-id: C5.S1.XMD5.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11300 / rank
 
Normal rank
Property / Symbols used: Q11300 / qualifier
 
Defining formula:

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

W
Property / Symbols used: Q11300 / qualifier
 
xml-id: C5.S20.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11303 / rank
 
Normal rank
Property / Symbols used: Q11303 / qualifier
 
Defining formula:

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

\psi_{n}(\beta)
Property / Symbols used: Q11303 / qualifier
 
xml-id: C5.S20.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11304 / rank
 
Normal rank
Property / Symbols used: Q11304 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta=1/(\BoltzmannConstant T)}

\beta=1/(\BoltzmannConstant T)
Property / Symbols used: Q11304 / qualifier
 
xml-id: C5.S20.XMD5.m1dec

Latest revision as of 01:12, 2 January 2020

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DLMF:5.20.E3
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{n}(\beta)=\int_{\Reals^{n}}e^{-\beta W}\diff{x}\\ =(2\pi)^{n/2}\beta^{-(n/2)-(\beta n(n-1)/4)}\*\left(\EulerGamma@{1+\tfrac{1}{2}\beta}\right)^{-n}\prod_{j=1}^{n}\EulerGamma@{1+\tfrac{1}{2}j\beta}.}
    0 references
    DLMF id
    DLMF:5.20.E3
    0 references
    Symbols used
    gamma function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
    xml-id
    C5.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
    Q10770
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    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
    Q10771
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q10812
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Reals}
    xml-id
    introduction.Sx4.p2.t1.r14.m2adec
    0 references
    Q11292
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j}
    xml-id
    C5.S1.XMD1.m1adec
    0 references
    Q11274
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C5.S1.XMD3.m1bdec
    0 references
    Q11281
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C5.S1.XMD5.m1bdec
    0 references
    Q11300
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W}
    xml-id
    C5.S20.XMD1.m1bdec
    0 references
    Q11303
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{n}(\beta)}
    xml-id
    C5.S20.XMD4.m1dec
    0 references
    Q11304
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta=1/(\BoltzmannConstant T)}
    xml-id
    C5.S20.XMD5.m1dec
    0 references
     
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