Paper Info
Title
New approximations of the gamma function in terms of the digamma function
Abstract
The goal of this paper is to prove the following asymptotic formula Γ(x)≈2πe−b(x+b)xexp(−x−12ψ(x+c)) as x∈N,x→∞, where Γ is the Euler Gamma function and ψ is the digamma function, namely, the logarithmic derivative of Γ. Moreover, optimal values of parameters b,c are calculated in such a way that this asymptotic convergence is the best possible.
Year
DOI
Venue
2010
10.1016/j.aml.2009.08.012
Applied Mathematics Letters
Keywords
Field
DocType
Gamma function,Digamma function,Speed of convergence
Asymptotic formula,Mathematical analysis,Digamma function,Approximations of π,Euler's formula,Logarithm,Polygamma function,Gamma function,Mathematics,Logarithmic derivative
Journal
Volume
Issue
ISSN
23
1
0893-9659
Citations 
PageRank 
References 
27
3.38
2
Authors
1
Name
Order
Citations
PageRank
Cristinel Mortici126739.13