DLMF:27.11.E2 (Q8071)

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DLMF:27.11.E2
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    Statements

    Defining formula
    ∑ n ≤ x d ⁡ ( n ) = x ⁢ ln ⁡ x + ( 2 ⁢ γ - 1 ) ⁢ x + O ⁡ ( x ) , subscript 𝑛 𝑥 divisor-function-D 𝑛 𝑥 𝑥 2 1 𝑥 Big-O 𝑥 {\displaystyle{\displaystyle\sum_{n\leq x}d\left(n\right)=x\ln x+(2\gamma-1)x+% O\left(\sqrt{x}\right),}}
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    DLMF id
    DLMF:27.11.E2
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    constraint
    x ≥ 2 𝑥 2 {\displaystyle{\displaystyle x\geq 2}}
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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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    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
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    Q12240
    Defining formula
    d k ⁡ ( n ) divisor-function-D 𝑘 𝑛 {\displaystyle{\displaystyle d_{\NVar{k}}\left(\NVar{n}\right)}}
    xml-id
    C27.S2.SS1.p4.m12adec
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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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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1adec
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    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1adec
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