Banach Journal of Mathematical Analysis

Complete monotonicity of a function involving the ratio of gamma functions and applications

Bai-Ni Guo, Feng Qi, and Chun-Fu Wei

Full-text: Open access

Abstract

In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result of Guo and Qi [Taiwanese J. Math. 7 (2003), no. 2, 239--247] and others. As applications, several inequalities involving the volume of the unit ball in $\mathbb{R}^n$ are derived, which refine, generalize and extend some known inequalities.

Article information

Source
Banach J. Math. Anal., Volume 6, Number 1 (2012), 35-44.

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1337014663

Digital Object Identifier
doi:10.15352/bjma/1337014663

Mathematical Reviews number (MathSciNet)
MR2862541

Zentralblatt MATH identifier
1245.33003

Subjects
Primary: 33B15: Gamma, beta and polygamma functions
Secondary: 26A48: Monotonic functions, generalizations 26A51: Convexity, generalizations 26D07: Inequalities involving other types of functions

Keywords
Necessary and sufficient condition logarithmically completely monotonic function gamma function volume of unit ball

Citation

Qi, Feng; Wei, Chun-Fu; Guo, Bai-Ni. Complete monotonicity of a function involving the ratio of gamma functions and applications. Banach J. Math. Anal. 6 (2012), no. 1, 35--44. doi:10.15352/bjma/1337014663. https://projecteuclid.org/euclid.bjma/1337014663


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