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A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums

Published online by Cambridge University Press:  17 February 2009

Feng Qi
Feng Qi
Affiliation:
College of Mathematics and Information Science, Henan University, Kaifeng City, Henan Province, 475001, China. Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China; e-mail: qifeng618@gmail.com, qifeng618@hotmail.com
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Abstract

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In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sums is found, and an equivalent relation between complete monotonicity and one of the class of inequalities is established.

Keywords

completely monotonic functionpsi functionpolygamma functioninequalitysumequivalence
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 4 , April 2007 , pp. 523 - 532
Copyright
Copyright © Australian Mathematical Society 2007

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