DLMF:19.23.E8 (Q6479)

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DLMF:19.23.E8
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    Statements

    Defining formula
    R - a ⁡ ( 𝐛 ; 𝐳 ) = 2 B ⁡ ( b 1 , b 2 ) ⁢ ∫ 0 π / 2 ( z 1 ⁢ cos 2 ⁡ θ + z 2 ⁢ sin 2 ⁡ θ ) - a ⁢ ( cos ⁡ θ ) 2 ⁢ b 1 - 1 ⁢ ( sin ⁡ θ ) 2 ⁢ b 2 - 1 ⁢ d θ , Carlson-integral-R 𝑎 𝐛 𝐳 2 Euler-Beta subscript 𝑏 1 subscript 𝑏 2 superscript subscript 0 𝜋 2 superscript subscript 𝑧 1 2 𝜃 subscript 𝑧 2 2 𝜃 𝑎 superscript 𝜃 2 subscript 𝑏 1 1 superscript 𝜃 2 subscript 𝑏 2 1 𝜃 {\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{2}% {\mathrm{B}\left(b_{1},b_{2}\right)}\int_{0}^{\pi/2}{(z_{1}{\cos^{2}}\theta+z_% {2}{\sin^{2}}\theta)}^{-a}\*(\cos\theta)^{2b_{1}-1}(\sin\theta)^{2b_{2}-1}% \mathrm{d}\theta,}}
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    DLMF id
    DLMF:19.23.E8
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    constraint
    ℜ ⁡ z 1 , ℜ ⁡ z 2 > 0 subscript 𝑧 1 subscript 𝑧 2 0 {\displaystyle{\displaystyle\Re z_{1},\Re z_{2}>0}}
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