DLMF:6.16.E5 (Q2314): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec

Revision as of 00:35, 2 January 2020

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DLMF:6.16.E5
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    Statements

    test
    li ⁡ ( x ) - π ⁢ ( x ) = O ⁡ ( x ⁢ ln ⁡ x ) , logarithmic-integral 𝑥 𝜋 𝑥 Big-O 𝑥 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(x\right)-\pi(x)=O\left(\sqrt{x}% \ln x\right),}}
    0 references
    DLMF id
    DLMF:6.16.E5
    0 references
    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}}
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    logarithmic integral
    test
    li ⁡ ( x ) logarithmic-integral 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.E8.m2adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
     
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