𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Gamma function inequalities

✍ 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.


πŸ“œ SIMILAR VOLUMES


Logarithmic Convexity and Inequalities f
✍ Milan Merkle πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 132 KB

We propose a method, based on logarithmic convexity, for producing sharp Ž . Ž . bounds for the ratio ⌫ x q ␀ r⌫ x . As an application, we present an inequality that sharpens and generalizes inequalities due to Gautschi, Chu, Boyd, Lazarevic-Ĺupas ¸, and Kershaw.

Inequalities for the gamma function with
✍ Peter J. Grabner; Robert F. Tichy; Uwe T. Zimmermann πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 548 KB

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

A generalization of some inequalities fo
✍ Biagio Palumbo πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 572 KB

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

A harmonic mean inequality for the gamma
✍ Horst Alzer πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 123 KB

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).