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DLMF:27.2.E3 - MaRDI portal

DLMF:27.2.E3 (Q8683)

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DLMF:27.2.E3
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    Statements

    DLMF defining formula
    π ⁡ ( x ) ∼ x ln ⁡ x . asymptotically-equals number-of-primes-less-pi 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\pi\left(x\right)\sim\frac{x}{\ln x}.}}
    0 references
    Symbols used
    asymptotic equality
    DLMF defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    number of primes not exceeding $$x$$
    DLMF defining formula
    π ⁡ ( x ) number-of-primes-less-pi 𝑥 {\displaystyle{\displaystyle\pi\left(\NVar{x}\right)}}
    xml-id
    C27.S2.E2.m2aadec
    0 references
    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1adec
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    Identifiers

     
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