Gamma function inequalities
β Scribed by Horst Alzer
- Publisher
- Springer US
- Year
- 2008
- Tongue
- English
- Weight
- 516 KB
- Volume
- 49
- Category
- Article
- ISSN
- 1017-1398
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We propose a method, based on logarithmic convexity, for producing sharp Ε½ . Ε½ . bounds for the ratio β« x q β€ rβ« x . As an application, we present an inequality that sharpens and generalizes inequalities due to Gautschi, Chu, Boyd, Lazarevic-ΔΉupas ΒΈ, and Kershaw.
The best known upper bound on the permanent of a O-l matrix relies on the knowledge of the number of nonzero entries per row. In certain applications only the total number of nonzero entries is known. In order to derive bounds in this situation we prove that the function f:( -1, co) + l%, defined by
Laforgia (1984) obtained some inequalities of the type according to the values of the positive parameters ~ and 2, valid for every non-negative real value of k, or at least for k greater than or equal than a k o depending on a and 2. In this paper a complete analysis of the problem is carried ou
We prove that for all positive real numbers x ~ 1, the harmonic mean of (F(x)) 2 and (F(1/x)) 2 is greater than 1. This refines a result of Gautschi (1974).