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).
A generalization of some inequalities for the gamma function
β Scribed by Biagio Palumbo
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 572 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0377-0427
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β¦ Synopsis
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 out, in order to establish, for fixed 0Β’ and 2, which of the two former inequalities holds, and for which values ofk. ~. t-E3 1997 Elsevier Science B.V. All rights reserved.
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