DLMF:6.16.E5 (Q2314)

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DLMF:6.16.E5
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    Statements

    Defining formula
    li ⁡ ( x ) - π ⁢ ( x ) = O ⁡ ( x ⁢ ln ⁡ x ) , logarithmic-integral 𝑥 𝜋 𝑥 Big-O 𝑥 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(x\right)-\pi(x)=O\left(\sqrt{x}% \ln x\right),}}
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    DLMF id
    DLMF:6.16.E5
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    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}}
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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.m2aadec
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    logarithmic integral
    Defining formula
    li ⁡ ( x ) logarithmic-integral 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.E8.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.m2adec
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    Q11307
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1edec
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    Q11311
    Defining formula
    π ⁢ ( x ) 𝜋 𝑥 {\displaystyle{\displaystyle\pi(x)}}
    xml-id
    C6.S16.XMD3.m1dec
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