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

DOI10.15352/bjma/1342210165zbMath1245.33004OpenAlexW2034424857MaRDI QIDQ437730

Qiu-Ming Luo, Feng Qi

Publication date: 18 July 2012

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjma/1342210165

zbMATH Keywords

gamma functionbound\(q\)-gamma functionlogarithmically completely monotonic functionratio of two gamma functions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Laplace transform (44A10) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48) (q)-gamma functions, (q)-beta functions and integrals (33D05) Other analytical inequalities (26D20)

Related Items (25)

Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ An inequality involving the gamma and digamma functions ⋮ Some best approximation formulas and inequalities for the Wallis ratio ⋮ Complete monotonicity for a new ratio of finitely many gamma functions ⋮ Complete monotonicity of two functions involving the tri- and tetra-gamma functions ⋮ The Function (b x − a x )∕x: Ratio’s Properties ⋮ Some properties of central Delannoy numbers ⋮ Integral representations of the Catalan numbers and their applications ⋮ Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function ⋮ On cumulative Tsallis entropies ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ Integral representations and properties of Stirling numbers of the first kind ⋮ Complete monotonicity of functions connected with the exponential function and derivatives ⋮ Some inequalities for the trigamma function in terms of the digamma function ⋮ Complete monotonicity of functions involving the \(q\)-trigamma and \(q\)-tetragamma functions ⋮ Bounds for the ratio of two gamma functions: from Wendel's asymptotic relation to Elezović-Giordano-Pečarić's theorem ⋮ Some conditions for a class of functions to be completely monotonic ⋮ Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body ⋮ A class of completely monotonic functions involving the gamma and polygamma functions ⋮ CERTAIN INEQUALITIES INVOLVING THE Q-DEFORMED GAMMA FUNCTION ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Some properties of the Fuss-Catalan numbers ⋮ An integral representation, complete monotonicity, and inequalities of the Catalan numbers ⋮ Asymptotic formulas and inequalities for the gamma function in terms of the tri-gamma function ⋮ An inequality for the gamma function via statistics and applications

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