DLMF:35.5.E3 (Q9796)

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DLMF:35.5.E3
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    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},}}
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    DLMF id
    DLMF:35.5.E3
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    constraint
    ν ∈ ℂ 𝜈 {\displaystyle{\displaystyle\nu\in\mathbb{C}}}
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    ν ∈ ℂ 𝜈 ℂ {\displaystyle{\displaystyle\nu\in\mathbb{C}}}
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    𝐓 ∈ 𝛀 𝐓 𝛀 {\displaystyle{\displaystyle\mathbf{T}\in{\boldsymbol{\Omega}}}}
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    Symbols used
    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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