DLMF:19.12.E7 (Q7001)

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DLMF:19.12.E7
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    Statements

    DLMF defining formula
    R C ⁡ ( x , y ) = 1 2 ⁢ x ⁢ ( ( 1 + y 2 ⁢ x ) ⁢ ln ⁡ ( 4 ⁢ x y ) - y 2 ⁢ x ) ⁢ ( 1 + O ⁡ ( y 2 / x 2 ) ) , Carlson-integral-RC 𝑥 𝑦 1 2 𝑥 1 𝑦 2 𝑥 4 𝑥 𝑦 𝑦 2 𝑥 1 Big-O superscript 𝑦 2 superscript 𝑥 2 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{1}{2\sqrt{x}}\left(% \left(1+\frac{y}{2x}\right)\ln\left(\frac{4x}{y}\right)-\frac{y}{2x}\right)\*(% 1+O\left(y^{2}/x^{2}\right)),}}
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    constraint
    y / x → 0 → 𝑦 𝑥 0 {\displaystyle{\displaystyle y/x\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.m2acdec
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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.m2acdec
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    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
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    Identifiers

     
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