A complete monotonicity property of the gamma function

By Feng Qi (祁锋), Chao Chen. 2004

196 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d0bdef1f4927836898b88b369ffdfad7cbf06203

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Refinements of lower bounds for polygamma functions (2009, background): “∈ N on I. In [18, Theorem 4], it was proved that all logarithmically completely monotonic functions are also completely monotonic, but not conversely. This result was formally published when revising [15]. For more information, please refer to [7, 20]. Lemma 2. The inequality ψ′(t) <e1/t−1 (16) h”
Logarithmically completely monotonic functions relating to the gamma function (2006, background): “The notion “logarithmically completely monotonic function” was posed explicitly in [25] and published formally in [24] and a much useful and meaningful relation L ⊂ C between the completely monotonic functions and the logarithmically completely monotonic functions was proved in [24,25].”
A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application (2006, unknown): “It was proved explicitly in [10, 42, 45, 46, 53] by different approaches that any logarithmically completely monotonic function must be completely monotonic, but not conversely.”
A PROPERTY OF LOGARITHMICALLY ABSOLUTELY MONOTONIC FUNCTIONS AND THE LOGARITHMICALLY COMPLETE MONOTONICITY OF A POWER-EXPONENTIAL FUNCTION (2009, background): “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.”
Three classes of logarithmically completely monotonic functions involving gamma and psi functions (2007, background): “Recall [1, 6, 12, 15, 17, 19, 20] also that a positive function f is called logarithmically completely monotonic on an interval I if f has derivatives of all orders on I and its logarithm ln f satisfies 0 ≤ (−1)k[ln f(x)] < ∞ for all k ∈ N on I.”
The Best Bounds in Gautschi-Kershaw Inequalities (2006, unknown): “([ 2, 14, 15, 16 ]) A logarithmically completely monotonic function is also completely monotonic.”
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].”
Bounds for the Ratio of Two Gamma Functions (2009, background): “This terminology was explicitly recovered in the preprints of [38, 41, 43].”
Some completely monotonic functions involving the gamma and polygamma functions (2006, background): “To the best of our knowledge, the terminology or the notion 'logarithmically completely monotonic function' was explicitly introduced in [5, 6, 7] and it was also”