Results 21 to 30 of about 14,913 (164)

On rational bounds for the gamma function

Journal of Inequalities and Applications, 2017
In the article, we prove that the double inequality x 2 + p 0 x + p 0 < Γ ( x + 1 ) < x 2 + 9 / 5 x + 9 / 5 $$ \frac{x^{2}+p_{0}}{x+p_{0}}< \Gamma(x+1)< \frac{x^{2}+9/5}{x+9/5} $$ holds for all x ∈ ( 0 , 1 ) $x\in(0, 1)$ , we present the best possible ...
Zhen-Hang Yang, Wei-Mao Qian, Yu-Ming Chu, Wen Zhang   +3 more
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Comparison of visual quantities in untrained neural networks

Cell Reports, 2023
Summary: The ability to compare quantities of visual objects with two distinct measures, proportion and difference, is observed even in newborn animals.
Hyeonsu Lee, Woochul Choi, Dongil Lee, Se-Bum Paik   +3 more
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Completely Monotone Functions: A Digest [PDF]

, 2014
To appear in: K. Alladi, G.V. Milovanovic and M. Th. Rassias (Eds.): "Analytic Number Theory, Approximation Theory and Special Functions", Special Volume dedicated to Professor Hari M.
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Completely Monotonic and Related Functions: Their Applications [PDF]

Journal of Applied Mathematics, 2014
Completely monotonic and related functions are important function classes inmathematical analysis. It was Bernstein [1] who in 1914 first introduced the notion of completely monotonic function. This year we celebrate its 100th anniversary. In 1921, Hausdorff [2] gave the notion of completely monotonic sequence, which is related to the notion of ...
Senlin Guo, Andrea Laforgia, Necdet Batir, Qiu-Ming Luo   +3 more
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q-Completely monotonic and q-Bernstein functions [PDF]

Journal of Applied Mathematics, Statistics and Informatics, 2014
Abstract We introduce the q-Bernstein functions, for 0<q<1 , and give sufficient and necessary conditions for a function to belong to the class of q -Bernstein functions. For some classes of functions we give results concerning q - completely monotonic and q -Bernstein functions.
Kokologiannaki, Chrysi G., Krasniqi, Valmir   +1 more
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Short Remarks on Complete Monotonicity of Some Functions

Mathematics, 2020
In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1
Ladislav Matejíčka
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Complete Monotonicity of Modified Bessel Functions [PDF]

Proceedings of the American Mathematical Society, 1990
We prove that if ν > 1 / 2 \nu > 1/2 , then 2 ν − 1 Γ ( ν ) / [ x ν
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A conjecture concerning a completely monotonic function

Computers & Mathematics with Applications, 2010
Based on a sequence of numerical computations, a conjecture is presented regarding the class of functions $H(x;a)=\exp(a)-(1+a/x)^x$, and the open problem of determining the values of $a$ for which the functions are completely monotonic with respect to $x$.
Shemyakova, E., Khashin, S.I., Jeffrey, D.J.   +2 more
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MONOTONICITY AND CONVEXITY PROPERTIES OF THE NIELSEN’S β-FUNCTION

Проблемы анализа, 2017
The Nielsen’s β-function provides a powerful tool for evaluating and estimating certain integrals, series and mathematical constants. It is related to other special functions such as the digamma function, the Euler’s beta function and the Gauss ...
Kwara Nantomah
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A class of completely monotonic functions involving the polygamma functions

Journal of Inequalities and Applications, 2022
Let Γ ( x ) $\Gamma (x)$ denote the classical Euler gamma function. We set ψ n ( x ) = ( − 1 ) n − 1 ψ ( n ) ( x ) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$ ( n ∈ N $n\in \mathbb{N}$ ), where ψ ( n ) ( x ) $\psi ^{(n)}(x)$ denotes the nth derivative of the
Li-Chun Liang, Li-Fei Zheng, Aying Wan
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