DLMF:27.11.E12 (Q8081): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2akdec

Revision as of 14:27, 2 January 2020

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DLMF:27.11.E12
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    Statements

    Defining formula
    ∑ n ≤ x μ ⁡ ( n ) = O ⁡ ( x ⁢ e - C ⁢ ln ⁡ x ) , subscript 𝑛 𝑥 Moebius-mu 𝑛 Big-O 𝑥 superscript 𝑒 𝐶 𝑥 {\displaystyle{\displaystyle\sum_{n\leq x}\mu\left(n\right)=O\left(xe^{-C\sqrt% {\ln x}}\right),}}
    0 references
    DLMF id
    DLMF:27.11.E12
    0 references
    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2akdec
    0 references
     
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