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Distributional boundary values of analytic functions and positive definite distributions
Nonlinear Analysis, 2015 We propose necessary and sufficient conditions for a distribution (generalized function) fof several variables to be positive definite. For this purpose, certain analytic extensions of f to tubular domains in complex space Cn are studied. The main result
Saulius Norvidas
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On some complete monotonic functions
, 2022 Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function",we confirm among other results and disprove other one.
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Some properties of the k-Gamma function
Le Matematiche, 2013 We give completely monotonicity properties and inequalities for functions involving the Γ_k functions and their logarithmic derivatives ψ_k functions.
Chrysi G. Kokologiannaki +1 more
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Monotonicity and inequalities for the gamma function
Journal of Inequalities and Applications, 2017 In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x ↦ 1 24 x ( ln Γ ( x + 1 / 2 ) − x ln x + x − ln 2 π ) + 1 − 120 7 x 2 $$ x\mapsto \frac{1}{24x ( \ln \Gamma ( x+1/2 ) -x\ln x+x- \ln \sqrt{
Zhen-Hang Yang, Jing-Feng Tian
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On complete monotonicity for several classes of functions related to ratios of gamma functions
Journal of Inequalities and Applications, 2019 Let Γ(x) $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative ψ(x)=[lnΓ(x)]′=Γ′(x)Γ(x) $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$, ψ′(x) $\psi '(x)$, and ψ″(x) $\psi ''(x)$ are, respectively ...
Feng Qi, Ravi P. Agarwal
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Logarithmically completely monotonic functions involving the Generalized Gamma Function
Le Matematiche, 2010 By a simple approach, two classes of functions involving generalization Euler's gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi ...
Faton Merovci, Valmir Krasniqi
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On completely monotonic functions
Let $ f:(0,\infty)\rightarrow \Bbb{R} $ be a completely monotonic function. In this paper, we present some properties of this functions and several new classes of completely monotonic functions. We also give some special functions such that its have completely monotonic condition.
Najafi, Mostafa, Morassaei, Ali
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Complete monotonicity of log-functions
Analysis and Mathematical PhysicsAbstract In this article we investigate the property of complete monotonicity within a special family $$\mathcal {F}_s$$ F s
Rourou Ma, Julian Weigert
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An inequality for completely monotone functions
, 2022 An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
Bitsouni, Vasiliki +2 more
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A New Criterion for Completely Monotonic Functions [PDF]
Transactions of the American Mathematical Society, 1944 Not ...
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