DLMF:35.6.E8 (Q9809)

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DLMF:35.6.E8
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    Statements

    Defining formula
    ∫ 𝛀 | 𝐓 | c - 1 2 ⁢ ( m + 1 ) ⁢ Ψ ⁡ ( a ; b ; 𝐓 ) ⁢ d 𝐓 = Γ m ⁡ ( c ) ⁢ Γ m ⁡ ( a - c ) ⁢ Γ m ⁡ ( c - b + 1 2 ⁢ ( m + 1 ) ) Γ m ⁡ ( a ) ⁢ Γ m ⁡ ( a - b + 1 2 ⁢ ( m + 1 ) ) , subscript 𝛀 superscript 𝐓 𝑐 1 2 𝑚 1 confluent-hypergeometric-of-matrix-Psi 𝑎 𝑏 𝐓 𝐓 multivariate-Euler-Gamma 𝑚 𝑐 multivariate-Euler-Gamma 𝑚 𝑎 𝑐 multivariate-Euler-Gamma 𝑚 𝑐 𝑏 1 2 𝑚 1 multivariate-Euler-Gamma 𝑚 𝑎 multivariate-Euler-Gamma 𝑚 𝑎 𝑏 1 2 𝑚 1 {\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}|\mathbf{T}|^{c-\frac{1}% {2}(m+1)}\Psi\left(a;b;\mathbf{T}\right)\mathrm{d}\mathbf{T}=\frac{\Gamma_{m}% \left(c\right)\Gamma_{m}\left(a-c\right)\Gamma_{m}\left(c-b+\frac{1}{2}(m+1)% \right)}{\Gamma_{m}\left(a\right)\Gamma_{m}\left(a-b+\frac{1}{2}(m+1)\right)},}}
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    DLMF id
    DLMF:35.6.E8
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    constraint
    ℜ ⁡ ( a ) > ℜ ⁡ ( c ) + 1 2 ⁢ ( m - 1 ) > m - 1 𝑎 𝑐 1 2 𝑚 1 𝑚 1 {\displaystyle{\displaystyle\Re(a)>\Re(c)+\frac{1}{2}(m-1)>m-1}}
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    ℜ ⁡ ( c - b ) > - 1 𝑐 𝑏 1 {\displaystyle{\displaystyle\Re(c-b)>-1}}
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    Symbols used
    confluent hypergeometric function of matrix argument (second kind)
    Defining formula
    Ψ ⁡ ( a ; b ; 𝐓 ) confluent-hypergeometric-of-matrix-Psi 𝑎 𝑏 𝐓 {\displaystyle{\displaystyle\Psi\left(\NVar{a};\NVar{b};\NVar{\mathbf{T}}% \right)}}
    xml-id
    C35.S6.E2.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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