DLMF:35.6.E5 (Q9806): 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: generalized hypergeometric function of matrix argument / rank
 
Normal rank
Property / Symbols used: generalized hypergeometric function of matrix argument / qualifier
 
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}}}}

\genhyperFmat{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{\mathbf{T}}}
Property / Symbols used: generalized hypergeometric function of matrix argument / qualifier
 
xml-id: C35.S8.E1.m2acdec
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.m1abdec
Property / Symbols used
 
Property / Symbols used: Q12718 / rank
 
Normal rank
Property / Symbols used: Q12718 / qualifier
 
Defining formula:

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

\exptrace@{\NVar{\mathbf{X}}}
Property / Symbols used: Q12718 / qualifier
 
xml-id: C35.S1.p3.t1.r10.m3abdec
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.m3abdec
Property / Symbols used
 
Property / Symbols used: Q12725 / rank
 
Normal rank
Property / Symbols used: Q12725 / qualifier
 
Defining formula:

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

\multivarEulerGamma{\NVar{m}}@{\NVar{a}}
Property / Symbols used: Q12725 / qualifier
 
xml-id: C35.S3.SS1.m1abdec
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.m1acdec
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: Q12734 / rank
 
Normal rank
Property / Symbols used: Q12734 / qualifier
 
Defining formula:

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

\mathbf{S}
Property / Symbols used: Q12734 / qualifier
 
xml-id: C35.S1.XMD10.m1dec
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.m1ddec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12720 / rank
 
Normal rank
Property / Symbols used: Q12720 / 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: Q12720 / qualifier
 
xml-id: C35.S1.XMD13.m1adec
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: 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 13:55, 2 January 2020

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DLMF:35.6.E5
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{\boldsymbol{\Omega}}\exptrace@{-\mathbf{T}\mathbf{X}}|\mathbf{X}|^{b-\frac{1}{2}(m+1)}\genhyperFmat{1}{1}@@{a}{b}{\mathbf{S}\mathbf{X}}\diff{\mathbf{X}}=\multivarEulerGamma{m}@{b}|\mathbf{I}-\mathbf{S}\mathbf{T}^{-1}|^{-a}|\mathbf{T}|^{-b},}
    0 references
    DLMF id
    DLMF:35.6.E5
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(b)}>\frac{1}{2}(m-1)}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{T}>\mathbf{S}}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Re(b)>\frac{1}{2}(m-1)}
    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.m2acdec
    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.m1abdec
    0 references
    Q12718
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exptrace@{\NVar{\mathbf{X}}}}
    xml-id
    C35.S1.p3.t1.r10.m3abdec
    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.m3abdec
    0 references
    Q12725
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \multivarEulerGamma{\NVar{m}}@{\NVar{a}}}
    xml-id
    C35.S3.SS1.m1abdec
    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.m1acdec
    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
    Q12734
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{S}}
    xml-id
    C35.S1.XMD10.m1dec
    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.m1ddec
    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.m1bdec
    0 references
    Q12720
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\boldsymbol{\Omega}}}
    xml-id
    C35.S1.XMD13.m1adec
    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
    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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