Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614915 | Journal of Mathematical Analysis and Applications | 2016 | 12 Pages |
Abstract
We consider differences between logΓ(x)logΓ(x) and truncations of certain classical asymptotic expansions in inverse powers of x−λx−λ whose coefficients are expressed in terms of Bernoulli polynomials Bn(λ)Bn(λ), and we obtain conditions under which these differences are strictly completely monotonic. In the symmetric cases λ=0λ=0 and λ=1/2λ=1/2, we recover results of Sonin, Nörlund and Alzer. Also we show how to derive these asymptotic expansions using the functional equation of the logarithmic derivative of the Euler gamma function, the representation of 1/x1/x as a difference F(x+1)−F(x)F(x+1)−F(x), and a backward induction.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Harold G. Diamond, Armin Straub,