DLMF:35.5.E3 (Q9796): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12718 / rank
 
Normal rank
Property / Symbols used: Q12718 / qualifier
 
Defining formula:

etr ⁡ ( 𝐗 ) exponential-trace 𝐗 {\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}

\exptrace@{\NVar{\mathbf{X}}}
Property / Symbols used: Q12718 / qualifier
 
xml-id: C35.S1.p3.t1.r10.m3adec
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.m3adec
Property / Symbols used
 
Property / Symbols used: Q12724 / rank
 
Normal rank
Property / Symbols used: Q12724 / qualifier
 
Defining formula:

𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}

\mathbf{T}
Property / Symbols used: Q12724 / qualifier
 
xml-id: C35.S1.XMD11.m1adec
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.m1dec
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.m1dec
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.m1bdec

Latest revision as of 14:52, 2 January 2020

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DLMF:35.5.E3
No description defined

    Statements

    Defining formula
    B ν ⁡ ( 𝐓 ) = ∫ 𝛀 etr ⁡ ( - ( 𝐓𝐗 + 𝐗 - 1 ) ) ⁢ | 𝐗 | ν - 1 2 ⁢ ( m + 1 ) ⁢ d 𝐗 , Bessel-of-matrix-B 𝜈 𝐓 subscript 𝛀 exponential-trace 𝐓𝐗 superscript 𝐗 1 superscript 𝐗 𝜈 1 2 𝑚 1 𝐗 {\displaystyle{\displaystyle B_{\nu}\left(\mathbf{T}\right)=\int_{\boldsymbol{% \Omega}}\mathrm{etr}\left(-(\mathbf{T}\mathbf{X}+\mathbf{X}^{-1})\right)|% \mathbf{X}|^{\nu-\frac{1}{2}(m+1)}\mathrm{d}\mathbf{X},}}
    0 references
    DLMF id
    DLMF:35.5.E3
    0 references
    constraint
    ν ∈ ℂ 𝜈 {\displaystyle{\displaystyle\nu\in\mathbb{C}}}
    0 references
    ν ∈ ℂ 𝜈 ℂ {\displaystyle{\displaystyle\nu\in\mathbb{C}}}
    0 references
    𝐓 ∈ 𝛀 𝐓 𝛀 {\displaystyle{\displaystyle\mathbf{T}\in{\boldsymbol{\Omega}}}}
    0 references
    Symbols used
    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
    0 references
    Q12718
    Defining formula
    etr ⁡ ( 𝐗 ) exponential-trace 𝐗 {\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}
    xml-id
    C35.S1.p3.t1.r10.m3adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q12724
    Defining formula
    𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}
    xml-id
    C35.S1.XMD11.m1adec
    0 references
    Q12719
    Defining formula
    𝐗 𝐗 {\displaystyle{\displaystyle\mathbf{X}}}
    xml-id
    C35.S1.XMD12.m1dec
    0 references
    Q12720
    Defining formula
    𝛀 𝛀 {\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}
    xml-id
    C35.S1.XMD13.m1dec
    0 references
    Q12723
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C35.S1.XMD8.m1bdec
    0 references
     
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