New Stirling-Type Approximations for the Gamma Function

Authors

Mansour Mahmoud Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia https://orcid.org/0000-0002-5918-1913
Hanan Almuashi Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah, 21589, Saudi Arabia
Cristinel Mortici Valahia University of Târgoviște, Târgoviște, 130004, Romania; Academy of Romanian Scientists, Bucharest, 050044, Romania; National University for Science and Technology Politehnica of Bucharest, Bucharest, 060042, Romania

DOI:

https://doi.org/10.37256/cm.6620258270

Keywords:

gamma function, Stirling’s formula, rate of convergence, inequalities

Abstract

This paper presents a set of new and precise Stirling-type formulas that approximate the Gamma function and provide associated sharp bounds. The proposed approximations are constructed using ratios of monic polynomials of even degree. In conclusion, an open question is raised regarding the general structure of such Gamma function approximations.

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Published

2025-11-26

Issue

Contemporary Mathematics, Volume 6 Issue 6 (2025)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.