DLMF:27.11.E3 (Q8072)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:27.11.E3
No description defined

    Statements

    Defining formula
    ∑ n ≤ x d ⁡ ( n ) n = 1 2 ⁢ ( ln ⁡ x ) 2 + 2 ⁢ γ ⁢ ln ⁡ x + O ⁡ ( 1 ) , subscript 𝑛 𝑥 divisor-function-D 𝑛 𝑛 1 2 superscript 𝑥 2 2 𝑥 Big-O 1 {\displaystyle{\displaystyle\sum_{n\leq x}\frac{d\left(n\right)}{n}=\frac{1}{2% }(\ln x)^{2}+2\gamma\ln x+O\left(1\right),}}
    0 references
    DLMF id
    DLMF:27.11.E3
    0 references
    constraint
    x ≥ 2 𝑥 2 {\displaystyle{\displaystyle x\geq 2}}
    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.m2abdec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
    0 references
    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.m12aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1bdec
    0 references
    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8072&oldid=46945"