Formula:2597

Digital Library of Mathematical Functions ID 5.4.E20

${\displaystyle{\displaystyle x_{n}=-n+\frac{1}{\pi}\operatorname{arctan}\left(\frac{\pi}{\ln n}\right)+O\left(\frac{1}{n(\ln n)^{2}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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