DLMF:35.6.E4 (Q9805)

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DLMF:35.6.E4
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    Statements

    Defining formula
    F 1 1 ⁡ ( a b ; 𝐓 ) = 1 B m ⁡ ( a , b - a ) ⁢ ∫ 𝟎 < 𝐗 < 𝐈 etr ⁡ ( 𝐓𝐗 ) ⁢ | 𝐗 | a - 1 2 ⁢ ( m + 1 ) ⁢ | 𝐈 - 𝐗 | b - a - 1 2 ⁢ ( m + 1 ) ⁢ d 𝐗 , Gauss-hypergeometric-of-matrix-pFq 1 1 𝑎 𝑏 𝐓 1 multivariate-Euler-Beta 𝑚 𝑎 𝑏 𝑎 subscript 0 𝐗 𝐈 exponential-trace 𝐓𝐗 superscript 𝐗 𝑎 1 2 𝑚 1 superscript 𝐈 𝐗 𝑏 𝑎 1 2 𝑚 1 𝐗 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=% \frac{1}{\mathrm{B}_{m}\left(a,b-a\right)}\int\limits_{\boldsymbol{{0}}<% \mathbf{X}<\mathbf{I}}\mathrm{etr}\left(\mathbf{T}\mathbf{X}\right)|\mathbf{X}% |^{a-\frac{1}{2}(m+1)}|\mathbf{I}-\mathbf{X}|^{b-a-\frac{1}{2}(m+1)}\mathrm{d}% \mathbf{X},}}
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    DLMF id
    DLMF:35.6.E4
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    constraint
    ℜ ⁡ ( a ) , ℜ ⁡ ( b - a ) > 1 2 ⁢ ( m - 1 ) 𝑎 𝑏 𝑎 1 2 𝑚 1 {\displaystyle{\displaystyle\Re(a),\Re(b-a)>\frac{1}{2}(m-1)}}
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