DLMF:35.8.E4 (Q10518)

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DLMF:35.8.E4
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    Statements

    DLMF defining formula
    A ν ⁡ ( 𝐓 ) = 1 Γ m ⁡ ( ν + 1 2 ⁢ ( m + 1 ) ) ⁢ F 1 0 ⁡ ( - ν + 1 2 ⁢ ( m + 1 ) ; - 𝐓 ) , Bessel-of-matrix-A 𝜈 𝐓 1 multivariate-Euler-Gamma 𝑚 𝜈 1 2 𝑚 1 Gauss-hypergeometric-of-matrix-pFq 0 1 𝜈 1 2 𝑚 1 𝐓 {\displaystyle{\displaystyle A_{\nu}\left(\mathbf{T}\right)=\dfrac{1}{\Gamma_{% m}\left(\nu+\frac{1}{2}(m+1)\right)}{{}_{0}F_{1}}\left({-\atop\nu+\frac{1}{2}(% m+1)};-\mathbf{T}\right),}}
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    constraint
    𝐓 ∈ 𝓢 𝐓 𝓢 {\displaystyle{\displaystyle\mathbf{T}\in\boldsymbol{\mathcal{S}}}}
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    Symbols used
    Q12738
    DLMF defining formula
    A ν ⁡ ( 𝐓 ) Bessel-of-matrix-A 𝜈 𝐓 {\displaystyle{\displaystyle A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S5.SS1.m1adec
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    generalized hypergeometric function of matrix argument
    DLMF defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; 𝐓 ) Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S8.E1.m2acdec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    Q12728
    DLMF defining formula
    Γ m ⁡ ( a ) multivariate-Euler-Gamma 𝑚 𝑎 {\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}
    xml-id
    C35.S3.SS1.m1adec
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    space of real symmetric matrices
    DLMF defining formula
    𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}
    xml-id
    C35.S1.XMD11.m1cdec
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    positive integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C35.S1.XMD8.m1dec
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    matrix of zeros
    DLMF defining formula
    𝓢 𝓢 {\displaystyle{\displaystyle\boldsymbol{\mathcal{S}}}}
    xml-id
    C35.S1.XMD9.m1adec
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    Identifiers

     
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