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On values of the psi function [PDF]

Journal of Applied Mathematics and Computational Mechanics, 2017
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Marcin Adam, Bożena Piątek, Mariusz Pleszczyński, Barbara Smoleń, Roman Wituła   +4 more
doaj   +2 more sources

ON FUNCTIONAL INEQUALITIES FOR THE PSI FUNCTION

Проблемы анализа
Motivated by the works of Bougotta and Mercer, the authors in this paper study the monotonicity of the function x↦ψ(1+bx)^a/ψ(1+ax)^b, and establish several inequalities involving the psi function.
Barkat A. Bhayo, Liyao Xie, Sebnem Yildiz Yar   +2 more
doaj   +3 more sources

A Novel Approach Using Serious Game Data to Predict the WISC-V Processing Speed Index in Children With Attention-Deficit/Hyperactivity Disorder: Machine Learning Study

JMIR Serious Games
BackgroundThe processing speed index (PSI) of the Korean Wechsler Intelligence Scale for Children-Fifth Edition (K-WISC-V) is highly correlated with symptoms of attention-deficit/hyperactivity disorder (ADHD) and is an important indicator of cognitive ...
Jun-Su Kim, Yoo Joo Jeong, Seung-Jae Kim, Su Jin Jun, Jin-Yeop Park, Hyang-Sook Hoe, Jeong-Heon Song   +6 more
doaj   +2 more sources

Anomalous experiences, psi and functional neuroimaging [PDF]

Frontiers in Human Neuroscience, 2013
Over the past decade, there has been increasing scientific interest in anomalous experiences. These can be defined as “uncommon experience[s] […] that, although [they] may be experienced by a significant number of persons […], [are] believed to deviate from ordinary experience or from the usually accepted explanation of reality according to Western ...
Acunzo, David, Evrard, Renaud, Rabeyron, Thomas   +2 more
openaire   +4 more sources

Chebyshev Approximations for the Psi Function [PDF]

Mathematics of Computation, 1973
Rational Chebyshev approximations to the psi (digamma) function are presented for .5 ≦ x ≦ 3.0 .5 \leqq x \leqq 3.0 , and 3.0 ≦ x 3.0 \leqq x . Maximum relative errors range down to the order of 10 − 20
Cody, W. J., Strecok, Anthony J., Thacher, Henry C. jun.   +2 more
openaire   +1 more source

Common properties and approximations of local function and set operator $\psi$

Cumhuriyet Science Journal, 2020
Through this paper, we shall obtain common properties of local functionand set operator $\psi$ and introduce the approximations of local function and set operator $\psi$.We also determined expansion of local function and set operator $\psi$ .
Shyamapada Modak, Sk Selim, Md. Monirul Islam   +2 more
doaj   +1 more source

An inequality for generalized complete elliptic integral

Journal of Inequalities and Applications, 2017
In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.
Li Yin, Li-Guo Huang, Yong-Li Wang, Xiu-Li Lin   +3 more
doaj   +1 more source

Improvements of the bounds for Ramanujan constant function

Journal of Inequalities and Applications, 2016
In the article, we establish several inequalities for the Ramanujan constant function R ( x ) = − 2 γ − ψ ( x ) − ψ ( 1 − x ) $R(x)=-2\gamma-\psi(x)-\psi(1-x)$ on the interval ( 0 , 1 / 2 ] $(0, 1/2]$ , where ψ ( x ) $\psi(x)$ is the classical psi ...
Hong-Hu Chu, Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu   +3 more
doaj   +1 more source

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
doaj   +1 more source

Monotonicity of some functions involving the gamma and psi functions [PDF]

Mathematics of Computation, 2008
The purpose of this paper is to deduce new inequalities for ratios of gamma functions; differences of digamma and polygamma functions, obtained via monotonicity of certain special functions, and indicate some applications of the derived inequalities in the estimation of certain trigonometric sums.
Koumandos, S., Koumandos, S.
openaire   +3 more sources