DLMF:19.2.E21 (Q6117)

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DLMF:19.2.E21
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    Statements

    Defining formula
    R C ⁡ ( x , y ) = ∫ 0 1 ( v 2 ⁢ x + ( 1 - v 2 ) ⁢ y ) - 1 / 2 ⁢ d v , Carlson-integral-RC 𝑥 𝑦 superscript subscript 0 1 superscript superscript 𝑣 2 𝑥 1 superscript 𝑣 2 𝑦 1 2 𝑣 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\int_{0}^{1}(v^{2}x+(1-v^{2% })y)^{-1/2}\mathrm{d}v,}}
    0 references
    DLMF id
    DLMF:19.2.E21
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    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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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
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