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Logarithmically completely monotonic functions related to the q-gamma function and its applications
Analysis and Mathematical Physics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khaled Mehrez, Sourav Das
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Logarithmically completely monotonic functions concerning gamma and digamma functions
Integral Transforms and Special Functions, 2007For given real numbers a≥0, b∈ℝ and c∈ℝ, let F a, b, c (x)=[Γ(x+1)]1/x (1+a/x) x+b /x c and φ a, b, c (x)=ψ″(x)+[2+(b+c)x−2x 2]/x 3+[3a(2a−b)+(6a−b)x+2x 2]/(x+a)3 with x∈(0, ∞), where Γ(x) and ψ(x) are the well-known Euler gamma function and the psi or digamma function, respectively.
Feng Qi, Wing-Sum Cheung
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Three classes of logarithmically completely monotonic functions involving gamma and psi functions [PDF]
Integral Transforms and Special Functions, 2007 By a simple approach, two classes of functions involving Euler’s gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi function is showed to be completely monotonic.
Feng Qi
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A class of logarithmically completely monotonic functions related to the gamma function with applications [PDF]
Integral Transforms and Special Functions, 2012 In this article, a necessary and sufficient condition and a necessary condition are established for a class of functions involving the gamma function to be logarithmically completely monotonic on . As applications of the necessary and sufficient condition, several two-sided bounding inequalities for the psi and polygamma functions and the ratio of two ...
Feng Qi +2 more
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FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION [PDF]
Journal of the Korean Mathematical Society, 2008 In this paper, two classes of functions, involving a parameter and the classical Euler gamma function, and two functions, involving the classical Euler gamma function, are verified to be logarithmically completely monotonic in or ; some inequalities involving the classical Euler gamma function are deduced and compared with those originating from ...
Feng Qi, Da-Wei Niu
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Integral Transforms and Special Functions, 2007
In this article, necessary and sufficient conditions under which two classes of functions are, respectively, logarithmically completely monotonic and completely monotonic are presented. From these conditions, several two-sided inequalities for the ratio of two gamma functions are deduced.
Feng Qi +2 more
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In this article, necessary and sufficient conditions under which two classes of functions are, respectively, logarithmically completely monotonic and completely monotonic are presented. From these conditions, several two-sided inequalities for the ratio of two gamma functions are deduced.
Feng Qi +2 more
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Applied Mathematics and Computation, 2008
Sufficient and necessary conditions are presented that a class of functions involving ratios of Euler's gamma function and originating from Wendel's and Gautschi's inequalities are logarithmically completely monotonic. From this, Wendel's, Gautschi's, Kershaw's, Laforgia's, Bustoz-Ismail's, Merkle's and Elezović-Giordano-Pečarić's inequalities are ...
Bai-Ni Guo, Feng Qi
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Sufficient and necessary conditions are presented that a class of functions involving ratios of Euler's gamma function and originating from Wendel's and Gautschi's inequalities are logarithmically completely monotonic. From this, Wendel's, Gautschi's, Kershaw's, Laforgia's, Bustoz-Ismail's, Merkle's and Elezović-Giordano-Pečarić's inequalities are ...
Bai-Ni Guo, Feng Qi
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A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions [PDF]
Positivity, 2018 15 ...
Khaled Mehrez
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COMPLETELY MONOTONIC FUNCTIONS RELATED TO LOGARITHMIC DERIVATIVES OF ENTIRE FUNCTIONS
Analysis and Applications, 2011The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity of functions related to Euler's psi-function.
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Two logarithmically completely monotonic functions involving logarithmic function
Mathematical Inequalities & ApplicationsTian-Yu Zhang, Ai-Ping Ji, Feng Qi
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