DLMF:19.23.E9 (Q6480)

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DLMF:19.23.E9
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    R - a ( 𝐛 ; 𝐳 ) = 4 Γ ( b 1 + b 2 + b 3 ) Γ ( b 1 ) Γ ( b 2 ) Γ ( b 3 ) 0 π / 2 0 π / 2 ( j = 1 3 z j l j 2 ) - a j = 1 3 l j 2 b j - 1 sin θ d θ d ϕ , Carlson-integral-R 𝑎 𝐛 𝐳 4 Euler-Gamma subscript 𝑏 1 subscript 𝑏 2 subscript 𝑏 3 Euler-Gamma subscript 𝑏 1 Euler-Gamma subscript 𝑏 2 Euler-Gamma subscript 𝑏 3 superscript subscript 0 𝜋 2 superscript subscript 0 𝜋 2 superscript superscript subscript 𝑗 1 3 subscript 𝑧 𝑗 superscript subscript 𝑙 𝑗 2 𝑎 superscript subscript product 𝑗 1 3 superscript subscript 𝑙 𝑗 2 subscript 𝑏 𝑗 1 𝜃 𝜃 italic-ϕ {\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{4% \Gamma\left(b_{1}+b_{2}+b_{3}\right)}{\Gamma\left(b_{1}\right)\Gamma\left(b_{2% }\right)\Gamma\left(b_{3}\right)}\int_{0}^{\pi/2}\!\!\!\!\int_{0}^{\pi/2}\left% (\sum_{j=1}^{3}z_{j}l_{j}^{2}\right)^{-a}\*\prod_{j=1}^{3}l_{j}^{2b_{j}-1}\sin% \theta\mathrm{d}\theta\mathrm{d}\phi,}}
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    DLMF:19.23.E9
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