Gamma and Factorial in the Monthly

Since its inception in 1894, the Monthly has printed 50 articles on the function or Stirling's asymptotic formula, including the magisterial 1959 paper by Phillip J. Davis, which won the 1963 Chauvenet prize, and the eye-opening 2000 paper by the Fields medalist Manjul Bhargava. In this article, we look back and comment on what has been said, and why, and try to guess what will be said about the function in future Monthly issues.(1) fn id=fn0001 It is a safe bet that there will be more proofs of Stirling's formula, for instance.fn We also identify some gaps, which surprised us: phase plots, Riemann surfaces, and the functional inverse of make their first appearance in the Monthly here. We also give a new elementary treatment of the asymptotics of n! and the first few terms of a new asymptotic formula for inv.