Results 1 to 10 of about 346 (88)
An accurate approximation formula for gamma function. [PDF]
J Inequal Appl, 2018 In this paper, we present a very accurate approximation for gamma function: \begin{equation*} \Gamma \left( x+1\right) \thicksim \sqrt{2\pi x}\left( \dfrac{x}{e}\right) ^{x}\left( x\sinh \frac{1}{x}\right) ^{x/2}\exp \left( \frac{7}{324}\frac{1}{ x^{3 ...
Yang ZH, Tian JF.
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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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Journal of Mathematical Inequalities, 2021 Let K (r) be the complete elliptic integral of the first kind. In this paper, we prove that the function Fp (x) = (1− x) expK ( √ x) is absolutely monotonic on (0,1) if and only if p π/8 , and −F ′ p (x) is absolutely monotonic on (0,1) if and only if 1 ...
Zhen-Hang Yang, Jing-feng Tian
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Mathematical Inequalities & Applications, 2021 In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives
Feng Qi (祁锋)
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Complete monotonicity of some functions involving k-digamma function with application
Journal of Mathematical Inequalities, 2021 We present several complete monotonicity properties involving k -digamma function with single parameter. These established results provide a k -generalization for the known results obtained by Burić and Elezović in [5]. Finally, we give an application to
L. Yin, Li-Guo Huang, Xiuli Lin
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Veterinary Dermatology, Volume 34, Issue 6, Page 586-596, December 2023., 2023 Background – In clinical practice, the diagnosis of otitis externa (OE) normally is based on otoscopic examination and cytological findings, followed by empirical treatment with topic drugs. Biofilm‐producing bacteria are frequently present in OE, even if its presence is often underdiagnosed. Hypothesis/Objectives – The primary aim of this study was to
Luca Luciani +6 more
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Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem [PDF]
Journal of Inequalities and Applications, 2009 In the expository review and survey paper dealing with bounds for the ratio of two gamma functions, along one of the main lines of bounding the ratio of two gamma functions, the authors look back and analyze some known results, including Wendel’s ...
Feng Qi (祁锋), Qiu-Ming Luo
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Three families of two-parameter means constructed by trigonometric functions
Journal of Inequalities and Applications, 2013 In this paper, we establish three families of trigonometric functions with two parameters and prove their monotonicity and bivariate log-convexity. Based on them, three two-parameter families of means involving trigonometric functions, which include ...
Zhen-Hang Yang
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Monotonicity results and bounds for the inverse hyperbolic sine [PDF]
, 2009 In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine.
B-N Guo +14 more
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Best bounds for the Lambert W functions
Journal of Mathematical Inequalities, 2020 This paper is devoted to provide tractable closed-form upper and lower bounds for the two real branches of the Lambert W function W(z(t)) for all positive real variable t where z(t) is increasing function on (0,∞) and bounded by zero and −e−1 ...
A. Salem
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