Article ID Journal Published Year Pages File Type
6419830 Applied Mathematics and Computation 2016 12 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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