A Turan-type inequality for the gamma function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:350

Article

Felder, Giovanni¹ 

[1] Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland

关键词: Turan-type inequality;    Gamma function;    Psi function;   

DOI  :  10.1016/j.jmaa.2008.09.053

来源: Elsevier

【 摘 要 】

We prove that the following Turan-type inequality holds for Euler's gamma function. For all odd integers n >= 1 and real numbers x > 0 we have alpha <= Gamma((n-1))(X)Gamma((n+1))(X) - Gamma((n))(X)(2), with the best possible constant alpha = min(1.5 <= X <= 2) Gamma(X)(2)psi'(X) = 0.6358 ..... (C) 2008 Elsevier Inc. All rights reserved.

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