Remarks on some completely monotonic functions
โ Scribed by Stamatis Koumandos
- Book ID
- 108175450
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 90 KB
- Volume
- 324
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We study completely monotonic and related functions whose first N derivatives are definite on an interval. Let L L N denote the class of functions defined by
In the present paper, we establish necessary and sufficient conditions for the functions | respectively to be monotonic and completely monotonic on (0, โ), where i โ N, ฮฑ > 0 and ฮฒ โฅ 0 are scalars, and ฯ (i) (x) are polygamma functions.
The main object of this work is to give some conditions for a class of functions to be logarithmically completely monotonic. Our result is shown to be an extension of a result which was proven in the recent literature on this subject.