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

✍ Scribed by C. Giordano; A. Laforgia; J. Pečarić

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
343 KB
Volume
99
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 involve the psi function. Inequalities for the ratio of two gamma functions are useful, for example, to deduce Bernstein-type inequalities for ultraspherical polynomials. We give an example of this type.

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✍ 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