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Abstract and Applied Analysis
Volume 2014, Article ID 851213, 5 pages
http://dx.doi.org/10.1155/2014/851213
Research Article

Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives

1State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University, Jiaozuo, Henan 454010, China
2School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, Henan 454010, China

Received 25 January 2014; Accepted 20 March 2014; Published 15 April 2014

Academic Editor: Beong In Yun

Copyright © 2014 Chun-Fu Wei and Bai-Ni Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some complete monotonicity results that the functions are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive derivatives of these two functions are decreasing on are discovered. As applications of these newly discovered results, some complete monotonicity results concerning the polylogarithm are found. Finally a conjecture on the complete monotonicity of the above-mentioned ratios is posed.