Article ID Journal Published Year Pages File Type
4593388 Journal of Number Theory 2016 12 Pages PDF
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
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