✦ LIBER ✦

Inequalities for the gamma function

✍ Scribed by Necdet Batir

Publisher: Springer
Year: 2008
Tongue: English
Weight: 144 KB
Volume: 91
Category: Article
ISSN: 0003-889X
DOI: 10.1007/s00013-008-2856-9

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Logarithmic Convexity and Inequalities f

Logarithmic Convexity and Inequalities for the Gamma Function

✍ Milan Merkle 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 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

Inequalities for the gamma function with applications to permanents

✍ Peter J. Grabner; Robert F. Tichy; Uwe T. Zimmermann 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 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

A generalization of some inequalities for the gamma function

✍ Biagio Palumbo 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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

Unified treatment of Gautschi-Kershaw ty

Unified treatment of Gautschi-Kershaw type inequalities for the gamma function

✍ C. Giordano; A. Laforgia; J. Pečarić 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 343 KB

Gautschi, Kershaw, Lorch, Laforgia and other authors gave several inequalities for the ratio F(x + 1 )/F(x + s) where, as usual, F denotes the gamma function. In this paper we give a unified treatment of all their results and prove, among other things, new inequalities for the above ratio, which inv

Inequalities for the Gamma and Polygamma

Inequalities for the Gamma and Polygamma Functions

✍ H. Alzer 📂 Article 📅 1998 🏛 Vandenhoeck & Ruprecht 🌐 German ⚖ 335 KB

A harmonic mean inequality for the gamma

A harmonic mean inequality for the gamma function

✍ Horst Alzer 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 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).