New upper bounds of n!
1 Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 Department of Mathematics, Texas A&M University, Kingsville 700 University Blvd, Kingsville, TX 78363-8202, USA
3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Journal of Inequalities and Applications 2012, 2012:27 doi:10.1186/1029-242X-2012-27Published: 13 February 2012
In this article, we deduce a new family of upper bounds of n! of the form
We also proved that the approximation formula for big factorials has a speed of convergence equal to n-2m-3 for m = 1,2,3,..., which give us a superiority over other known formulas by a suitable choice of m.
Mathematics Subject Classification (2000): 41A60; 41A25; 57Q55; 33B15; 26D07.