DLMF:27.11.E15 (Q8084)

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DLMF:27.11.E15
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    Statements

    Defining formula
    lim x → ∞ ⁡ ∑ n ≤ x μ ⁡ ( n ) ⁢ ln ⁡ n n = - 1 . subscript → 𝑥 subscript 𝑛 𝑥 Moebius-mu 𝑛 𝑛 𝑛 1 {\displaystyle{\displaystyle\lim_{x\to\infty}\sum_{n\leq x}\frac{\mu\left(n% \right)\ln n}{n}=-1.}}
    0 references
    DLMF id
    DLMF:27.11.E15
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    Symbols used
    Möbius function
    Defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2acdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ajdec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1jdec
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    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1ndec
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