Gamma and Factorial in the Monthly. Issue 5 (28th May 2018)

• Record Type: Journal Article
• Authors: Borwein, Jonathan M.; Corless, Robert M.
• Is Part Of: American Mathematical Monthly. Volume 125:Issue 5(2018)
• Page Start: 400
• Page End: 424
• Publication Date: 2018-05-28
• Subjects: Primary 01-02 -- Secondary 33-02; 33-03; 33B15; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2018.1420983
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: Since its inception in 1894, theMonthly has printed 50 articles on the Γ 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 Γ function in futureMonthly issues. 1 We also identify some gaps, which surprised us: phase plots, Riemann surfaces, and the functional inverse of Γ make their first appearance in theMonthly here. We also give a new elementary treatment of the asymptotics of n ! and the first few terms of a new asymptotic formula for invΓ.