Remarks on some completely monotonic functions
Date
2006ISSN
0022-247XSource
Journal of Mathematical Analysis and ApplicationsVolume
324Issue
2Pages
1458-1461Google Scholar check
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Applying the Euler-Maclaurin summation formula, we obtain upper and lower polynomial bounds for the function frac(x, ex - 1), x > 0, with coefficients the Bernoulli numbers Bk. This enables us to give simpler proofs of some results of H. Alzer and F. Qi et al., concerning complete monotonicity of certain functions involving the gamma function Γ (x), the psi function ψ (x) and the polygamma functions ψ(n) (x), n = 1, 2, ... . © 2005 Elsevier Inc. All rights reserved.