Results 21 to 30 of about 88,745 (291)
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 +2 more
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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 +3 more
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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
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 +3 more
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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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The monotonicity and convexity of a function involving psi function with applications
Journal of Inequalities and Applications, 2016 In this paper, we prove that the function x ↦ exp ( ψ ( x + 1 2 ) − 1 24 1 x 2 + 7 / 40 ) − x $$ x\mapsto\exp \biggl( \psi \biggl( x+\frac{1}{2} \biggr) -\frac {1}{24} \frac{1}{x^{2}+7/40} \biggr) -x $$ is decreasing from ( − 1 / 2 , ∞ ) $( -1/2,\infty )
Bang-Cheng Sun +3 more
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Monotonicity and inequalities involving the incomplete gamma function
Journal of Inequalities and Applications, 2016 In the article, we deal with the monotonicity of the function x → [ ( x p + a ) 1 / p − x ] / I p ( x ) $x\rightarrow[ (x^{p}+a )^{1/p}-x]/I_{p}(x)$ on the interval ( 0 , ∞ ) $(0, \infty)$ for p > 1 $p>1$ and a > 0 $a>0$ , and present the necessary and ...
Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu
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Instability of standing waves for a quasi-linear Schrödinger equation in the critical case
AIMS Mathematics, 2022 We consider the following quasi-linear Schrödinger equation. $ \begin{align} i\frac{\partial\psi}{\partial t}+\triangle\psi+\psi\triangle|\psi|^2+|\psi|^{p-1}\psi = 0,x\in \mathbb{R}^D, D\geq1, \;\;\;\;\;\;\;\;\;(Q)\end{align} $ where $ \psi ...
Xiaoguang Li, Chaohe Zhang
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Padé approximant related to asymptotics for the gamma function
Journal of Inequalities and Applications, 2017 Based on the Padé approximation method, we determine the coefficients a j $a_{j}$ and b j $b_{j}$ ( 1 ≤ j ≤ k $1\leq j\leq k$ ) such that Γ ( x + 1 ) 2 π x ( x / e ) x = x k + a 1 x k − 1 + ⋯ + a k x k + b 1 x k − 1 + ⋯ + b k + O ( 1 x 2 k + 1 ) , x → ∞ ,
Xin Li, Chao-Ping Chen
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Optimal bounds for the generalized Euler–Mascheroni constant
Journal of Inequalities and Applications, 2018 We provide several sharp upper and lower bounds for the generalized Euler–Mascheroni constant. As consequences, some previous bounds for the Euler–Mascheroni constant are improved.
Ti-Ren Huang +3 more
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