Volume 11 Number 4 (Oct. 2021)
Home > Archive > 2021 > Volume 11 Number 4 (Oct. 2021) >
IJAPM 2021 Vol.11(4): 61-70 ISSN: 2010-362X
DOI: 10.17706/ijapm.2021.11.4.61-70

Simple but High-Accuracy Approximations for n!

Steven Pigeon

Abstract—Computing n! efficiently and accurately is notoriously difficult. Many have proposed approximations, varying in accuracy and in computational complexity. Interesting and useful approxi¬mations are both accurate and computationally inexpensive, and, if possible, exact up to machine-precision floating-point numbers. In this paper, we exploit an observation on a previous approximation by Hodgman to obtain a new class of correction terms using simple, but optimal given their degree, rational functions. We show that the proposed approximations are more accurate than some of the best-known approximations while remaining computationally inexpensive.

Index Terms— Approximation, asymptotic error, factorial, rational function.

Steven Pigeon is with Department of Mathematics, Computer Science and Engineering, Université du Québec à Rimouski, Canada.

Cite:Steven Pigeon, "Simple but High-Accuracy Approximations for n!," International Journal of Applied Physics and Mathematics vol. 11, no. 4, pp. 61-70, 2021.

Copyright © 2021 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

General Information

ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca 
Abstracting/ Indexing: INSPEC(IET), CNKI, Google Scholar, EBSCO, Chemical Abstracts Services (CAS), etc.
E-mail: ijapm@iap.org
  • Dec 27, 2021 News!

    IJAPM Vol 9 & Vol 10 have been indexed by Inspec   [Click]

  • Jan 02, 2024 News!

    IJAPM will adopt Article-by-Article Work Flow For the Quarterly journal, each issue will be released at the end of the issue month

  • Jan 02, 2024 News!

    The papers published in Vol 13, No 4 has received dois from Crossref

  • Oct 09, 2023 News!

    IJAPM Vol 13, No 4 has been published with online version   [Click]

  • Oct 09, 2023 News!

    The papers published in Vol 13, No 3 has received dois from Crossref

  • Read more>>