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Some completely monotonic functions involving the gamma and polygamma functions

Part of: Elementary classical functions Inequalities

Published online by Cambridge University Press:  09 April 2009

Feng Qi ,
Bai-Ni Guo  and
Chao-Ping Chen
Feng Qi
Affiliation:
Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China, e-mail: qifeng@hpu.edu.cn, guobaini@hpu.edu.cn, chenchaoping@hpu.edu.cn
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Abstract

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The function [Γ(x + 1)]1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞). The function ψ″ (x + 2) + (1 + x2)/x2(1 + x)2 is strictly completely monotonic in (0, ∞).

Keywords

completely monotonic functionlogarithmically completely monotonic functiongamma functionpolygamma function.

MSC classification

Secondary: 33B15: Gamma, beta and polygamma functions 26D07: Inequalities involving other types of functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 1 , February 2006 , pp. 81 - 88
Copyright
Copyright © Australian Mathematical Society 2006

References

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