DLMF:19.27.E16 (Q6608)

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DLMF:19.27.E16
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    Statements

    Defining formula
    R J ⁡ ( x , y , z , p ) = ( 3 / x ) ⁢ R C ⁡ ( ( h + p ) 2 , 2 ⁢ ( b + h ) ⁢ p ) + O ⁡ ( 1 x 3 / 2 ⁢ ln ⁡ x b + h ) , Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 3 𝑥 Carlson-integral-RC superscript ℎ 𝑝 2 2 𝑏 ℎ 𝑝 Big-O 1 superscript 𝑥 3 2 𝑥 𝑏 ℎ {\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=(3/\sqrt{x})R_{C}\left(% (h+p)^{2},2(b+h)p\right)+O\left(\frac{1}{x^{3/2}}\ln\frac{x}{b+h}\right),}}
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    DLMF id
    DLMF:19.27.E16
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    constraint
    max ⁡ ( y , z , p ) / x → 0 → 𝑦 𝑧 𝑝 𝑥 0 {\displaystyle{\displaystyle\max(y,z,p)/x\to 0}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2andec
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    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.m2abdec
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    symmetric elliptic integral of third kind
    Defining formula
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2aedec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2agdec
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    Q11891
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C19.S27.XMD2.m1cdec
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    Q11890
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C19.S27.XMD6.m1edec
    0 references
     
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