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DLMF:19.27.E2 - MaRDI portal

DLMF:19.27.E2 (Q7290)

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DLMF:19.27.E2
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    Statements

    DLMF defining formula
    R F ⁡ ( x , y , z ) = 1 2 ⁢ z ⁢ ( ln ⁡ 8 ⁢ z a + g ) ⁢ ( 1 + O ⁡ ( a z ) ) , Carlson-integral-RF 𝑥 𝑦 𝑧 1 2 𝑧 8 𝑧 𝑎 𝑔 1 Big-O 𝑎 𝑧 {\displaystyle{\displaystyle R_{F}\left(x,y,z\right)=\frac{1}{2\sqrt{z}}\left(% \ln\frac{8z}{a+g}\right)\left(1+O\left(\frac{a}{z}\right)\right),}}
    0 references
    constraint
    a / z → 0 → 𝑎 𝑧 0 {\displaystyle{\displaystyle a/z\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.m2adec
    0 references
    symmetric elliptic integral of first kind
    DLMF defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2adec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    a
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C19.S27.XMD1.m1adec
    0 references
    g
    DLMF defining formula
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C19.S27.XMD5.m1adec
    0 references

    Identifiers

     
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