Formula:8774

Digital Library of Mathematical Functions ID 27.11.E12

${\displaystyle{\displaystyle\sum_{n\leq x}\mu\left(n\right)=O\left(xe^{-C\sqrt{\ln x}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle x\to\infty}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}$: Möbius function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real number
• ${\displaystyle{\displaystyle C}}$: constant
 

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