Banach Journal of Mathematical Analysis

Bounds for the ratio of two gamma functions---From Wendel's and related inequalities to logarithmically completely monotonic functions

Qiu-Ming Luo and Feng Qi

Full-text: Open access

Abstract

In the survey paper, along one of several main lines of bounding the ratio of two gamma functions, the authors retrospect and analyse Wendel's double inequality, Kazarinoff's refinement of Wallis' formula, Watson's monotonicity, Gautschi's double inequality, Kershaw's first double inequality, and the (logarithmically) complete monotonicity results of functions involving ratios of two gamma or $q$-gamma functions obtained by Bustoz, Ismail, Lorch, Muldoon, and other mathematicians.

Article information

Source
Banach J. Math. Anal., Volume 6, Number 2 (2012), 132-158.

Dates
First available in Project Euclid: 13 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1342210165

Digital Object Identifier
doi:10.15352/bjma/1342210165

Mathematical Reviews number (MathSciNet)
MR2945993

Zentralblatt MATH identifier
1245.33004

Subjects
Primary: 33B15: Gamma, beta and polygamma functions
Secondary: 26A48: Monotonic functions, generalizations 26A51: Convexity, generalizations 33D05: $q$-gamma functions, $q$-beta functions and integrals 26D20: Other analytical inequalities 44A10: Laplace transform 46-02: Research exposition (monographs, survey articles) 46F12: Integral transforms in distribution spaces [See also 42-XX, 44-XX] 46T20: Continuous and differentiable maps [See also 46G05]

Keywords
Bound ratio of two gamma functions logarithmically completely monotonic function gamma function $q$-gamma function

Citation

Qi, Feng; Luo, Qiu-Ming. Bounds for the ratio of two gamma functions---From Wendel's and related inequalities to logarithmically completely monotonic functions. Banach J. Math. Anal. 6 (2012), no. 2, 132--158. doi:10.15352/bjma/1342210165. https://projecteuclid.org/euclid.bjma/1342210165


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