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DLMF:27.11.E7 - MaRDI portal

DLMF:27.11.E7 (Q8769)

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DLMF:27.11.E7
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    Statements

    DLMF defining formula
    ∑ n ≤ x ϕ ⁡ ( n ) n = 6 π 2 ⁢ x + O ⁡ ( ln ⁡ x ) . subscript 𝑛 𝑥 Euler-totient-phi 𝑛 𝑛 6 2 𝑥 Big-O 𝑥 {\displaystyle{\displaystyle\sum_{n\leq x}\frac{\phi\left(n\right)}{n}=\frac{6% }{{\pi^{2}}}x+O\left(\ln x\right).}}
    0 references
    constraint
    x ≥ 2 𝑥 2 {\displaystyle{\displaystyle x\geq 2}}
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    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2afdec
    0 references
    Euler’s totient
    DLMF defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1fdec
    0 references
    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1fdec
    0 references

    Identifiers

     
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