Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593388 | Journal of Number Theory | 2016 | 12 Pages |
Abstract
In this paper, we establish a double inequality for the gamma function, from which we deduce the following approximation formula:Γ(x+1)∼2πx(xe)x(1+112x3+247x−12)x2+53210,x→∞, which is more accurate than the Burnside, Gosper, Ramanujan, Windschitl, and Nemes formulas. We develop the previous approximation formula to produce an asymptotic expansion.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chao-Ping Chen,