DLMF:35.3.E8 (Q9784): 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: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
Property / Symbols used
 
Property / Symbols used: multivariate beta function / rank
 
Normal rank
Property / Symbols used: multivariate beta function / qualifier
 
Defining formula:

B m ⁡ ( a , b ) multivariate-Euler-Beta 𝑚 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right% )}}

\multivarEulerBeta{\NVar{m}}@{\NVar{a}}{\NVar{b}}
Property / Symbols used: multivariate beta function / qualifier
 
xml-id: C35.S3.E3.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\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:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12726 / qualifier
 
xml-id: C35.S1.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q12719 / rank
 
Normal rank
Property / Symbols used: Q12719 / qualifier
 
Defining formula:

𝐗 𝐗 {\displaystyle{\displaystyle\mathbf{X}}}

\mathbf{X}
Property / Symbols used: Q12719 / qualifier
 
xml-id: C35.S1.XMD12.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12720 / rank
 
Normal rank
Property / Symbols used: Q12720 / qualifier
 
Defining formula:

𝛀 𝛀 {\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}

{\boldsymbol{\Omega}}
Property / Symbols used: Q12720 / qualifier
 
xml-id: C35.S1.XMD13.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12728 / rank
 
Normal rank
Property / Symbols used: Q12728 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q12728 / qualifier
 
xml-id: C35.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12723 / rank
 
Normal rank
Property / Symbols used: Q12723 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12723 / qualifier
 
xml-id: C35.S1.XMD8.m1gdec

Latest revision as of 14:49, 2 January 2020

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DLMF:35.3.E8
No description defined

    Statements

    Defining formula
    B m ⁡ ( a , b ) = ∫ 𝛀 | 𝐗 | a - 1 2 ⁢ ( m + 1 ) ⁢ | 𝐈 + 𝐗 | - ( a + b ) ⁢ d 𝐗 , multivariate-Euler-Beta 𝑚 𝑎 𝑏 subscript 𝛀 superscript 𝐗 𝑎 1 2 𝑚 1 superscript 𝐈 𝐗 𝑎 𝑏 𝐗 {\displaystyle{\displaystyle\mathrm{B}_{m}\left(a,b\right)=\int_{\boldsymbol{% \Omega}}|\mathbf{X}|^{a-\frac{1}{2}(m+1)}|\mathbf{I}+\mathbf{X}|^{-(a+b)}% \mathrm{d}\mathbf{X},}}
    0 references
    DLMF id
    DLMF:35.3.E8
    0 references
    constraint
    ℜ ⁡ ( a ) , ℜ ⁡ ( b ) > 1 2 ⁢ ( m - 1 ) 𝑎 𝑏 1 2 𝑚 1 {\displaystyle{\displaystyle\Re(a),\Re(b)>\frac{1}{2}(m-1)}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    multivariate beta function
    Defining formula
    B m ⁡ ( a , b ) multivariate-Euler-Beta 𝑚 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right% )}}
    xml-id
    C35.S3.E3.m2abdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
    0 references
    Q12726
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C35.S1.XMD1.m1edec
    0 references
    Q12719
    Defining formula
    𝐗 𝐗 {\displaystyle{\displaystyle\mathbf{X}}}
    xml-id
    C35.S1.XMD12.m1cdec
    0 references
    Q12720
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}
    xml-id
    C35.S1.XMD13.m1bdec
    0 references
    Q12728
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C35.S1.XMD2.m1bdec
    0 references
    Q12723
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C35.S1.XMD8.m1gdec
    0 references
     
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