Formula:8784

Digital Library of Mathematical Functions ID 27.12.E7

${\displaystyle{\displaystyle\left|\pi\left(x\right)-\mathrm{li}\left(x\right)\right|<\frac{1}{8\pi}\sqrt{x}\,\ln x.}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}$: logarithmic integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\pi\left(\NVar{x}\right)}}$: number of primes not exceeding $$x$$
• ${\displaystyle{\displaystyle x}}$: real number
 

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