Results 31 to 40 of about 346 (88)
Complete monotonicity properties and asymptotic expansions of the logarithm of the gamma function
, 2015 We prove two conjectures of Chen concerning the complete monotonicity properties of some functions involving the gamma and polygamma functions. We prove asymptotic expansions of the logarithm of the gamma function in terms of the polygamma functions, and
Chao Chen, Jing-Yun Liu
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Integral representation of some functions related to the Gamma function
, 2004 We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes ...
Berg, Christian
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SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
, 2016 . By employing a refined version of the P´olya type integralinequality and other techniques, the authors establish some inequalitiesand absolute monotonicity for modified Bessel functions of the first kindwith nonnegative integer order. 1. Main resultsIt is
Bai-Ni Guo (郭白妮), Feng Qi (祁锋)
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Generalizations of the Bell Numbers and Polynomials and Their Properties
, 2017 In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of ...
Feng Qi (祁锋) +3 more
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On complete monotonicity of some functions related to means
, 2013 We show the complete monotonicity of some functions related to the Stolarsky mean which was a problem of S.-X. Chen and F. Qi (2007) [15]. In the proof, the connection between operator monotone and completely monotonic functions is used.
Ádám Besenyei
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On the q-beta function inequalities
, 2015 In this paper, we provide some inequalities for the q -beta function with q > 0 by means of calculus and q -Čebyšev-Grüss type integral inequalities. When letting q → 1 , some of our results approach to results obtained by some authors and the others are
A. Salem
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A completely monotonic function involving the tri- and tetra-gamma functions
, 2010 The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function.
Guo, Bai-Ni, Qi, Feng
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EXPONENTIAL CONVEXITY OF THE FAVARD'S INEQUALITY AND RELATED RESULTS
, 2017 A b s t r a c t: In this paper we prove positive semi-definiteness of matrices generated by differences deduced from unweighted and weighted Favard's inequality. This implies a surprising property of exponential convexity of this differences which allows
N. Latif, J. Pečarić, I. Peric
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An involution inequality for the Kullback-Leibler divergence
, 2017 . Let Rt := t P + (1− t)Pι , where t ∈ (0,1) , P is a probability measure, and Pι is the push-forward image of P under a measurable involution ι . An inequality involving the Kullback–Leibler divergence of Rt from P is given. It is shown that the role of
I. Pinelis
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Logarithmically Completely Monotonic Ratios of Mean Values and an Application [PDF]
, 2005 In the article, some strictly Logarithmically completely monotonic ratios of mean values are ...
Chen, Chao-Ping, Qi, Feng
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