DLMF:27.11.E6 (Q8075)

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DLMF:27.11.E6
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    Statements

    Defining formula
    ∑ n ≤ x ϕ ⁡ ( n ) = 3 π 2 ⁢ x 2 + O ⁡ ( x ⁢ ln ⁡ x ) . subscript 𝑛 𝑥 Euler-totient-phi 𝑛 3 2 superscript 𝑥 2 Big-O 𝑥 𝑥 {\displaystyle{\displaystyle\sum_{n\leq x}\phi\left(n\right)=\frac{3}{{\pi^{2}% }}x^{2}+O\left(x\ln x\right).}}
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    DLMF id
    DLMF:27.11.E6
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    constraint
    x ≥ 2 𝑥 2 {\displaystyle{\displaystyle x\geq 2}}
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aedec
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    Euler’s totient
    Defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1edec
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    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1edec
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