Definition:Stirling's Constant

Definition

Stirling's constant is a name given to the square root of $2$ times $\pi$ (pi).

It is approximated by the decimal expansion:

$\sqrt {2 \pi} \approx 2 \cdotp 50662 \, 82746 \, 31000 \, 5 \ldots$

Source of Name

This entry was named for James Stirling.

Historical Note

The name Stirling's constant has been coined by $\mathsf{Pr} \infty \mathsf{fWiki}$ for the square root of $2 \pi$ from its appearance in Stirling's Formula, where it can be seen to be:

$\ds \sqrt {2 \pi} = \lim_{n \mathop \to \infty} \dfrac {n! e^n} {n^n \sqrt n}$