Formula:8781

Digital Library of Mathematical Functions ID 27.12.E4

${\displaystyle{\displaystyle\pi\left(x\right)\sim\sum_{k=1}^{\infty}\frac{(k-1)!\,x}{(\ln x)^{k}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\pi\left(\NVar{x}\right)}}$: number of primes not exceeding $$x$$
• ${\displaystyle{\displaystyle k}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real number
 

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