A Sterling Look at Stirling’s Constant

SummaryIn a previous article [3 Hammett, A. (2020). Euler’s limit and Stirling’s estimate. Coll. Math. J. 51(5): 330–336. DOI: 10.1080/07468342.2020.1811058.[Taylor & Francis Online] , [Google Scholar]] appearing in this journal, existence of the finite positive limit κ=limn→∞n!(en)nn−1/2 implicit in Stirling’s approximation n!≈2πn(ne)n was proved, and in so doing this limit was connected to the Euler limit limn→∞(1+1n)n=e. Because it was not done in the original article, exact determination of the constant κ (=2π) by a novel, elementary technique is the aim of this follow-up. For both articles, the arguments are readily accessible to advanced undergraduate students with a year of university calculus in their background.