## Abstract and Applied Analysis

### Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives

#### Abstract

Some complete monotonicity results that the functions ${\pm}1/({e}^{{\pm}t}-1)$ 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 $(0, \infty )$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 851213, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276911

Digital Object Identifier
doi:10.1155/2014/851213

Mathematical Reviews number (MathSciNet)
MR3198263

Zentralblatt MATH identifier
07023195

#### Citation

Wei, Chun-Fu; Guo, Bai-Ni. Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives. Abstr. Appl. Anal. 2014 (2014), Article ID 851213, 5 pages. doi:10.1155/2014/851213. https://projecteuclid.org/euclid.aaa/1412276911

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