Editing E (mathematical constant) (section)

=== Asymptotics ===
The number {{mvar|e}} occurs naturally in connection with many problems involving [[asymptotics]]. An example is [[Stirling's formula]] for the [[Asymptotic analysis|asymptotics]] of the [[factorial function]], in which both the numbers {{mvar|e}} and [[pi|{{pi}}]] appear:<ref name="greg">{{cite book|first=Greg |last=Gbur |author-link=Greg Gbur |year=2011 |title=Mathematical Methods for Optical Physics and Engineering |isbn=978-0-521516-10-5 |publisher=Cambridge University Press |page=779}}</ref>
<math display="block>n! \sim \sqrt{2\pi n} \left(\frac{n}{e}\right)^n.</math>

As a consequence,<ref name="greg"/>
<math display="block>e = \lim_{n\to\infty} \frac{n}{\sqrt[n]{n!}} .</math>