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DLMF:27.11.E15 - MaRDI portal

DLMF:27.11.E15 (Q8777)

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DLMF:27.11.E15
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    Statements

    DLMF 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
    Symbols used
    Möbius function
    DLMF defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2acdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ajdec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1jdec
    0 references
    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1ndec
    0 references

    Identifiers

     
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