Formula:3012

Digital Library of Mathematical Functions ID 6.16.E5

${\displaystyle{\displaystyle\mathrm{li}\left(x\right)-\pi(x)=O\left(\sqrt{x}\ln x\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}$: logarithmic integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\pi(x)}}$: number of primes ≤ x
 

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