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DLMF:27.12.E7 - MaRDI portal

DLMF:27.12.E7 (Q8784)

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DLMF:27.12.E7
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    Statements

    DLMF defining formula
    | π ⁡ ( x ) - li ⁡ ( x ) | < 1 8 ⁢ π ⁢ x ⁢ ln ⁡ x . number-of-primes-less-pi 𝑥 logarithmic-integral 𝑥 1 8 𝑥 𝑥 {\displaystyle{\displaystyle\left|\pi\left(x\right)-\mathrm{li}\left(x\right)% \right|<\frac{1}{8\pi}\sqrt{x}\,\ln x.}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    logarithmic integral
    DLMF defining formula
    li ⁡ ( x ) logarithmic-integral 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.E8.m2abdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aedec
    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.m2addec
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    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1ddec
    0 references

    Identifiers

     
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