DLMF:19.27.E7 (Q6599)

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DLMF:19.27.E7
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    Statements

    Defining formula
    R D ⁡ ( x , y , z ) = 3 2 ⁢ z 3 / 2 ⁢ ( ln ⁡ ( 8 ⁢ z a + g ) - 2 ) ⁢ ( 1 + O ⁡ ( a z ) ) , Carlson-integral-RD 𝑥 𝑦 𝑧 3 2 superscript 𝑧 3 2 8 𝑧 𝑎 𝑔 2 1 Big-O 𝑎 𝑧 {\displaystyle{\displaystyle R_{D}\left(x,y,z\right)=\frac{3}{2z^{3/2}}\left(% \ln\left(\frac{8z}{a+g}\right)-2\right)\left(1+O\left(\frac{a}{z}\right)\right% ),}}
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    DLMF id
    DLMF:19.27.E7
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    constraint
    a / z → 0 → 𝑎 𝑧 0 {\displaystyle{\displaystyle a/z\to 0}}
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aedec
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    elliptic integral symmetric in only two variables
    Defining formula
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2adec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
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    Q11888
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C19.S27.XMD1.m1cdec
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