Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 6, Number 2 (2012), 132-158.
Bounds for the ratio of two gamma functions---From Wendel's and related inequalities to logarithmically completely monotonic functions
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.
Banach J. Math. Anal., Volume 6, Number 2 (2012), 132-158.
First available in Project Euclid: 13 July 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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