Results 11 to 20 of about 257 (49)
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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The geometric mean is a Bernstein function [PDF]
, 2013 In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of $n$ positive numbers.
Li, Wen-Hui, Qi, Feng, Zhang, Xiao-Jing
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An alternative proof of Elezovi\'c-Giordano-Pe\v{c}ari\'c's theorem
, 2009 In the present note, an alternative proof is supplied for Theorem~1 in [N. Elezovi\'c, C. Giordano and J. Pe\v{c}ari\'c, \textit{The best bounds in Gautschi's inequality}, Math. Inequal. Appl.
Guo, Bai-Ni, Qi, Feng
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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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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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Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials [PDF]
, 2002 In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are ...
Luo, Qiu-Ming, Qi, Feng
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, 2012 In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete monotonicity ...
Qi, Feng
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On the Laplace transform of absolutely monotonic functions
, 2016 We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function.
Koumandos, Stamatis, Pedersen, Henrik L.
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A refinement of a double inequality for the gamma function
, 2011 In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.Comment: 8 ...
Guo, Bai-Ni, Qi, Feng
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New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations [PDF]
, 2007 In the paper, new upper bounds in the second Kershaw’s double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are ...
Guo, Senlin, Qi, Feng
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