DLMF:35.7.E5 (Q9816): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: multivariate beta function / rank
 
Normal rank
Property / Symbols used: multivariate beta function / qualifier
 
Defining formula:

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

\multivarEulerBeta{\NVar{m}}@{\NVar{a}}{\NVar{b}}
Property / Symbols used: multivariate beta function / qualifier
 
xml-id: C35.S3.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

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

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec
Property / Symbols used
 
Property / Symbols used: Q12726 / rank
 
Normal rank
Property / Symbols used: Q12726 / qualifier
 
Defining formula:

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

a
Property / Symbols used: Q12726 / qualifier
 
xml-id: C35.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12724 / rank
 
Normal rank
Property / Symbols used: Q12724 / qualifier
 
Defining formula:

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

\mathbf{T}
Property / Symbols used: Q12724 / qualifier
 
xml-id: C35.S1.XMD11.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12719 / rank
 
Normal rank
Property / Symbols used: Q12719 / qualifier
 
Defining formula:

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

\mathbf{X}
Property / Symbols used: Q12719 / qualifier
 
xml-id: C35.S1.XMD12.m1dec
Property / Symbols used
 
Property / Symbols used: Q12728 / rank
 
Normal rank
Property / Symbols used: Q12728 / qualifier
 
Defining formula:

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

b
Property / Symbols used: Q12728 / qualifier
 
xml-id: C35.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12736 / rank
 
Normal rank
Property / Symbols used: Q12736 / qualifier
 
Defining formula:

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

c
Property / Symbols used: Q12736 / qualifier
 
xml-id: C35.S1.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12723 / rank
 
Normal rank
Property / Symbols used: Q12723 / qualifier
 
Defining formula:

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

m
Property / Symbols used: Q12723 / qualifier
 
xml-id: C35.S1.XMD8.m1cdec

Latest revision as of 14:58, 2 January 2020

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DLMF:35.7.E5
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    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperFmat{2}{1}@@{a,b}{c}{\mathbf{T}}=\frac{1}{\multivarEulerBeta{m}@{a}{c-a}}\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I}}|\mathbf{X}|^{a-\frac{1}{2}(m+1)}\*{|\mathbf{I}-\mathbf{X}|}^{c-a-\frac{1}{2}(m+1)}{|\mathbf{I}-\mathbf{T}\mathbf{X}|}^{-b}\diff{\mathbf{X}},}
    0 references
    DLMF id
    DLMF:35.7.E5
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(a)},\realpart@@{(c-a)}>\frac{1}{2}(m-1)}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Re(a),\Re(c-a)>\frac{1}{2}(m-1)}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{0}}<\mathbf{T}<\mathbf{I}}
    0 references
    Symbols used
    generalized hypergeometric function of matrix argument
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperFmat{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{\mathbf{T}}}}
    xml-id
    C35.S8.E1.m2addec
    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
    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
    multivariate beta function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \multivarEulerBeta{\NVar{m}}@{\NVar{a}}{\NVar{b}}}
    xml-id
    C35.S3.E3.m2adec
    0 references
    Q10811
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q12726
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
    xml-id
    C35.S1.XMD1.m1cdec
    0 references
    Q12724
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{T}}
    xml-id
    C35.S1.XMD11.m1cdec
    0 references
    Q12719
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{X}}
    xml-id
    C35.S1.XMD12.m1dec
    0 references
    Q12728
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b}
    xml-id
    C35.S1.XMD2.m1cdec
    0 references
    Q12736
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c}
    xml-id
    C35.S1.XMD3.m1cdec
    0 references
    Q12723
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C35.S1.XMD8.m1cdec
    0 references
     
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