Completely monotonic functions involving the gamma and q-gamma functions

By Arcadii Z. Grinshpan, Mourad E. H. Ismail. 2005

117 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/235d06e7f12fb13cd72f356c8b8e62ace9c06d83

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In Applied Mathematics

1. Feng Qi (祁锋)
2. Bai-Ni Guo (郭白妮)
3. Necdet Batır
4. Dmitrii Karp
5. Hari M. Srivastava
6. Chao Chen
7. Bo-Yan Xi
8. Y. Chu

In Statistics and Probability

1. Feng Qi (祁锋)
2. Bai-Ni Guo (郭白妮)
3. Necdet Batır

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): “Recall also [4, 5, 8, 15, 17] that a positive function f is said to be logarithmically completely monotonic on an interval I if f has derivatives of all orders on I and (−1)[ln f(x)] ≥ 0 (3) for all x ∈ I and n ∈ N.”
• Inequalities for the gamma function (2008, background): “Recently numerous interesting inequalities for the gamma function have been proved by many mathematicians, we refer to [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 17, 20, 22], and the references therein.”
• A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application (2006, unknown): “ction or ratio in the literature, has been investigated since 1948 in [56] at least. Now there exist a lot of conclusions on Wallis ratio, its variants, generalizations and applications, for example, [2, 11, 21, 23, 24, 28, 30, 31, 32, 33, 34, 35, 40, 41, 44, 47, 48] and related references therein. ”
• Completely Monotonic Gamma Ratio and Infinitely Divisible H-Function of Fox (2015, background): “1 in [5] stating that q(x) = ∏p k=1 Γ k(x + λk) with ∑p k=1 σk = 0 and λk ≥ 0 is logarithmically completely monotone on (0,∞) if and only if v(t) = p ∑”
• Bounds for the Ratio of Two Gamma Functions (2009, background): “1] and [51, 124] 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 [59, Theorem 4.”
• Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity (2007, unknown): “In [21] Clark and Ismail introduced the functions Gm(x) = x mΨ(x) and Φm(x) = −xmΨ(m)(x).”
• 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.”