Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function

Chao-Ping Chen

Applied Mathematics and Computation, 2016, vol. 283, issue C, 385-396

Abstract: We define ϑ(x) by the equality Γ(x+1)=π(xe)x(8x3+4x2+x+130)1/6eϑ(x).We call ϑ(x) the remainder of Ramanujan’s formula. In this paper, we present some properties for ϑ(x), including monotonicity properties, inequalities and asymptotic expansions. Furthermore, we present some full asymptotic expansions for the gamma function related to the Nemes, Ramanujan and Burnside formulas.

Keywords: Gamma function; Asymptotic expansion; Inequality (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:283:y:2016:i:c:p:385-396

DOI: 10.1016/j.amc.2016.02.040

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