DLMF:19.2.E18 (Q6114)

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DLMF:19.2.E18
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    Statements

    Defining formula
    R C ⁡ ( x , y ) = 1 y - x ⁢ arctan ⁡ y - x x = 1 y - x ⁢ arccos ⁡ x / y , Carlson-integral-RC 𝑥 𝑦 1 𝑦 𝑥 𝑦 𝑥 𝑥 1 𝑦 𝑥 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{1}{\sqrt{y-x}}% \operatorname{arctan}\sqrt{\frac{y-x}{x}}=\frac{1}{\sqrt{y-x}}\operatorname{% arccos}\sqrt{x/y},}}
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    DLMF id
    DLMF:19.2.E18
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    constraint
    0 ≤ x < y 0 𝑥 𝑦 {\displaystyle{\displaystyle 0\leq x<y}}
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    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.m2aadec
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    Q11208
    Defining formula
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6adec
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    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7abdec
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