Some completely monotonic functions involving the gamma and polygamma functions

By Feng Qi (祁锋), Bai-Ni Guo (郭白妮), Ch. P. Chen. Journal of the Australian Mathematical Society, 2006

118 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/04f5befe2becf827ca653d3af8e438d95ee2623f

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In Applied Mathematics

Citations in the corpus

Completely monotonic functions involving the gamma and q-gamma functions (2005, background): “We call such functions f (x) logarithmically completely monotonic [8] [24] [25].”
Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity (2007, background): “6 Logarithmically completely monotonic functions In [24] the authors call a function f :]0,∞[→]0,∞[ logarithmically completely monotonic if it is C∞ and (−1)[log f(x)] ≥ 0, for k = 1, 2, .”
Three classes of logarithmically completely monotonic functions involving gamma and psi functions (2007, background): “1] and [6, 20] it is pointed out that the logarithmically completely monotonic functions on (0,∞) can be characterized as the infinitely divisible completely monotonic functions studied by Horn in [7, Theorem 4.”
Logarithmically completely monotonic functions relating to the gamma function (2006, background): “Motivated by the papers [25,26], among other things, it is proved in [9] that S \ {0} ⊂ L⊂ C.”
The Dagum family of isotropic correlation functions (2007, background): “The Dagum family of isotropic correlation functions 1137 In [10], the authors call a function f : ]0,∞[→]0,∞[ logarithmically completely monotonic if it is C and (−1)[log f(x)] ≥ 0 for x > 0, n= 1,2, .”
A PROPERTY OF LOGARITHMICALLY ABSOLUTELY MONOTONIC FUNCTIONS AND THE LOGARITHMICALLY COMPLETE MONOTONICITY OF A POWER-EXPONENTIAL FUNCTION (2009, methodology): “In [7, 38, 41, 43, 44, 52] and many other references, the inclusions CL[I] ⊂ C[I] and S ⊂ CL[(0,∞)] were revealed implicitly or explicitly, where S denotes the class of Stieltjes transforms.”
Bounds for the Ratio of Two Gamma Functions (2009, background): “This terminology was explicitly recovered in the preprints of [38, 41, 43].”
Integral Representation of Some Functions Related to the Gamma Function (2004, background): “Each of these statements imply the result of [12].”
TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION (2009, background): “For more information on the logarithmically completely monotonic functions, please refer to [5, 18] and related references therein.”
Some completely monotonic functions involving polygamma functions and an application (2005, background): “Recently, some completely monotonic properties of functions involving the gamma, psi, and polygamma functions are verified in [6, 7, 8, 9].”