Logarithmically completely monotonic functions relating to the gamma function

By Chao Chen, Feng Qi (祁锋). 2006

68 citations recorded by the source corpus.

Abstract In this paper, the logarithmically complete monotonicity of the function e x Γ ( x + β ) / x x + β − α in ( 0 , ∞ ) for α ∈ R and β ⩾ 0 is considered and the corresponding result by G.D. Anderson, R.W. Barnard, K.C. Richards, M.K. Vamanamurthy and M. Vuorinen is generalized. As applications of these results, some inequalities between identric mean and ratio of two gamma functions by J.D. Keckic and P.M. Vasic are extended.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/2c242ac1dad8c257c86892f5423c4c8e7a1525b9

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In Applied Mathematics

Citations in the corpus

A PROPERTY OF LOGARITHMICALLY ABSOLUTELY MONOTONIC FUNCTIONS AND THE LOGARITHMICALLY COMPLETE MONOTONICITY OF A POWER-EXPONENTIAL FUNCTION (2009, methodology): “These techniques have been used in [1, 2, 3, 5, 9, 10, 11, 12, 13, 14, 15, 17, 22, 28, 29, 30, 31, 32, 33, 36, 37, 40, 43, 44, 45, 48, 49, 50, 52, 56] and many other articles.”
TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION (2009, background): “In [6], the function e xΓ(x) x was proved to be logarithmically completely monotonic on (0,∞) if and only if α ≥ 1 and so was its reciprocal if and only if α ≤ 1 2 .”
Bounds for the Ratio of Two Gamma Functions (2009, background): “In 2006, the following necessary and sufficient conditions were demonstrated in [33]: For α ∈ R and β ≥ 0, the function fα,β(x) = eΓ(x + β) xx+β−α (5.”