## Abstract and Applied Analysis

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

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

#### Abstract

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

**Permanent link to this document**

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