DLMF:19.26.E17 (Q6574)

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DLMF:19.26.E17
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    Statements

    test
    α ⁢ R C ⁡ ( β , α + β ) + β ⁢ R C ⁡ ( α , α + β ) = π / 2 , 𝛼 Carlson-integral-RC 𝛽 𝛼 𝛽 𝛽 Carlson-integral-RC 𝛼 𝛼 𝛽 𝜋 2 {\displaystyle{\displaystyle\sqrt{\alpha}R_{C}\left(\beta,\alpha+\beta\right)+% \sqrt{\beta}R_{C}\left(\alpha,\alpha+\beta\right)=\pi/2,}}
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    DLMF id
    DLMF:19.26.E17
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    constraint
    α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}
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    α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 ℂ 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}
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    α + β > 0 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha+\beta>0}}
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    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    test
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2addec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10923
    test
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2adec
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