DLMF:35.8.E13 (Q9835)

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DLMF:35.8.E13
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    Statements

    Defining formula
    ∫ 𝟎 < 𝐗 < 𝐈 | 𝐗 | a 1 - 1 2 ⁢ ( m + 1 ) ⁢ | 𝐈 - 𝐗 | b 1 - a 1 - 1 2 ⁢ ( m + 1 ) ⁢ F q p ⁡ ( a 2 , … , a p + 1 b 2 , … , b q + 1 ; 𝐓𝐗 ) ⁢ d 𝐗 = 1 B m ⁡ ( b 1 - a 1 , a 1 ) ⁢ F q + 1 p + 1 ⁡ ( a 1 , … , a p + 1 b 1 , … , b q + 1 ; 𝐓 ) , subscript 0 𝐗 𝐈 superscript 𝐗 subscript 𝑎 1 1 2 𝑚 1 superscript 𝐈 𝐗 subscript 𝑏 1 subscript 𝑎 1 1 2 𝑚 1 Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 2 … subscript 𝑎 𝑝 1 subscript 𝑏 2 … subscript 𝑏 𝑞 1 𝐓𝐗 𝐗 1 multivariate-Euler-Beta 𝑚 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑎 1 Gauss-hypergeometric-of-matrix-pFq 𝑝 1 𝑞 1 subscript 𝑎 1 … subscript 𝑎 𝑝 1 subscript 𝑏 1 … subscript 𝑏 𝑞 1 𝐓 {\displaystyle{\displaystyle\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I% }}|\mathbf{X}|^{a_{1}-\frac{1}{2}(m+1)}{|\mathbf{I}-\mathbf{X}|}^{b_{1}-a_{1}-% \frac{1}{2}(m+1)}\*{{}_{p}F_{q}}\left({a_{2},\dots,a_{p+1}\atop b_{2},\dots,b_% {q+1}};\mathbf{T}\mathbf{X}\right)\mathrm{d}\mathbf{X}=\frac{1}{\mathrm{B}_{m}% \left(b_{1}-a_{1},a_{1}\right)}{{}_{p+1}F_{q+1}}\left({a_{1},\dots,a_{p+1}% \atop b_{1},\dots,b_{q+1}};\mathbf{T}\right),}}
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    DLMF id
    DLMF:35.8.E13
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    constraint
    ℜ ⁡ ( b 1 - a 1 ) , ℜ ⁡ ( a 1 ) > 1 2 ⁢ ( m - 1 ) subscript 𝑏 1 subscript 𝑎 1 subscript 𝑎 1 1 2 𝑚 1 {\displaystyle{\displaystyle\Re(b_{1}-a_{1}),\Re(a_{1})>\frac{1}{2}(m-1)}}
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