Article ID Journal Published Year Pages File Type
4593191 Journal of Number Theory 2016 10 Pages PDF
Abstract

Mortici (2015) [31] proposed a new formula for approximating the gamma function and the convergence of the corresponding asymptotic series is very fast in comparison with other classical or recently discovered asymptotic series. In this paper, by the Lagrange–Bürmann formula we give an explicit formula for determining the coefficients akak(k=1,2,…)(k=1,2,…) in Mortici's formula such thatΓ(x+1)2πx(xe)x∼exp⁡{∑k=1∞ak(x12x2+25)k},x→∞. Moreover, by the cycle indicator polynomial of symmetric group, we give an explicit expression for the coefficients bkbk(k=0,1,…)(k=0,1,…) of the following expansion:Γ(x+1)2πx(xe)x∼(∑k=0∞bk(x12x2+25)k)1/r,x→∞. A recursive formula for calculating the coefficients bkbk(k=0,1,…)(k=0,1,…) is also given.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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