DLMF:19.12.E6 (Q7000)

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DLMF:19.12.E6
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    Statements

    DLMF defining formula
    R C ⁡ ( x , y ) = π 2 ⁢ y - x y ⁢ ( 1 + O ⁡ ( x y ) ) , Carlson-integral-RC 𝑥 𝑦 𝜋 2 𝑦 𝑥 𝑦 1 Big-O 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{\pi}{2\sqrt{y}}-\frac% {\sqrt{x}}{y}\left(1+O\left(\sqrt{\frac{x}{y}}\right)\right),}}
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    constraint
    x / y → 0 → 𝑥 𝑦 0 {\displaystyle{\displaystyle x/y\to 0}}
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    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
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    Carlson’s combination of inverse circular and inverse hyperbolic functions
    DLMF 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.m2abdec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Identifiers

     
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