Some classes of completely monotonic functions (2002)
| Citations: | 11 - 4 self |
BibTeX
@MISC{Alzer02someclasses,
author = {Horst Alzer and Christian Berg},
title = {Some classes of completely monotonic functions},
year = {2002}
}
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Abstract
Abstract. A function f: (0, ∞) → R is said to be completely monotonic if (−1) n f (n) (x) ≥ 0 for all x> 0 and n = 0, 1, 2,.... In this paper we present several new classes of completely monotonic functions. Our functions have in common that they are defined in terms of the classical gamma, digamma, and polygamma functions. Moreover, we apply one of our monotonicity theorems to prove a new inequality for prime numbers. Some of the given results extend and complement theorems due to Bustoz & Ismail, Clark & Ismail, and other researchers. Key words. Complete monotonicity, gamma, digamma, and polygamma functions, prime numbers, inequalities. 2000 Mathematics Subject Classification. Primary 11A41, 26A48, 33B15; Secondary 26D15. 1.
Citations
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| 23 | On some inequalities for the gamma and psi functions - Alzer - 1997 |
| 9 | Quelques remarques sur le cône de Stieltjes, in: Séminaire de Théorie du Potentiel - Berg - 1980 |
| 8 | Some gamma function inequalities - Alzer - 1993 |
| 6 | Completely monotonic rational functions and Hall’s marriage theorem - Ball - 1994 |
