Gamma and Factorial in the Monthly

@article{Borwein2018GammaAF,
  title={Gamma and Factorial in the Monthly},
  author={Jonathan Michael Borwein and Robert M Corless},
  journal={The American Mathematical Monthly},
  year={2018},
  volume={125},
  pages={400 - 424}
}
Abstract Since its inception in 1894, the Monthly 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 future Monthly issues.11 It is a safe bet that there will be more proofs of… 
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Notes on the historical bibliography of the gamma function.
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References

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James Stirling's Methodus differentialis
Contains not only the results and ideas for which Stirling is chiefly remembered, for example, Stirling numbers and Stirling's asymptotic formula for factorials, but also a wealth of material on
A simple proof of Stirling's formula for the gamma function
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  • Mathematics
    The Mathematical Gazette
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where and the notation means that as . C = 2π f (n) ∼ g(n) f (n) / g(n) → 1 n → ∞ A great deal has been written about Stirling's formula. At this point I will just mention David Fowler's Gazette
Laplace's Integral, the Gamma Function, and beyond
TLDR
This article focuses on Laplace's basic result and his identity, and avoids popular techniques: "messy" contour integration and the theory of Fourier transforms, which invariably invokes the Fourier inversion formula.
The Gamma Function: An Eclectic Tour
TLDR
The gamma function was subjected to intense study by almost every eminent mathematician of the nineteenth and early twentieth centuries and continues to interest the present genera tion from the integral representation numerous identities including the beta-gamma relation and the duplication formula of Legendre were deduced.
Note on the Beta and Gamma Functions
In N. Bourbaki, IDlements de Mathematique, Fonctions d'une variable reelle, Ch. 1, 2, 3, 2me Md., 1958, p. 127, one finds a simple and interesting method of evaluating the Euler-Poisson integral f
The (n + 1)th Proof of Stirling's Formula
TLDR
In the following the author uses a skillful but not so obvious estimate of the In function to present a really elementary deduction of Stirling's formula.
Stirling's Series Made Easy
TLDR
The method is adapted to obtain Stirling's series for the logarithm of the gamma function and it is shown that the constants obtained are the best ones possible, i.e., they cannot be improved by any method whatsoever.
Graphing elementary Riemann surfaces
TLDR
This paper shows how to use a computer algebra system (or even a purely numerical graphing package) to graph the Riemann surfaces of various elementary functions.
James Stirling’s Methodus Differentialis: An annotated translation of Stirling’s text, by Ian Tweddle. Pp. 295. €129.95, £ 75.00, sFr 210.00, $ 129.00. 2003. ISBN 1 85233 723 0 (Springer).
classroom as well as Anthony Ferzola's account of Euler's use of differentials as 'absolute zeros', a non-rigorous intuitive approach which was exonerated in retrospect by Abraham Robinson's
Stirling's Formula via the Poisson Distribution
  • M. Pinsky
  • Mathematics, Computer Science
    Am. Math. Mon.
  • 2007
9. A. I. Katsevich and A. G. Ramm, The Radon Transform and Local Tomography, CRC Press, Boca Raton, FL, 1996. 10. E. Lindel?f, Calcul des R?sidus, Gauthier-Villars, Paris, 1905. 11. G.
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