DLMF:4.4.E19 (Q1553)

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DLMF:4.4.E19
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    Statements

    Defining formula
    lim n → ∞ ⁡ ( ( ∑ k = 1 n 1 k ) - ln ⁡ n ) = γ = 0.57721 56649 01532 86060 ⁢ … , subscript → 𝑛 subscript superscript 𝑛 𝑘 1 1 𝑘 𝑛 0.57721 56649 01532 86060 … {\displaystyle{\displaystyle\lim_{n\to\infty}\left(\left(\sum^{n}_{k=1}\frac{1% }{k}\right)-\ln n\right)=\gamma=0.57721\ 56649\ 01532\ 86060\dots,}}
    0 references
    DLMF id
    DLMF:4.4.E19
    0 references
    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aedec
    0 references
    Q11219
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1adec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1bdec
    0 references
     
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