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:

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

This sequence is A019727 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

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:

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

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 \cdotp 506 \, 628 \ldots$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2 \cdotp 50662 \, 8 \ldots$