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Common properties and approximations of local function and set operator $\psi$ [PDF]
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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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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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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Cross sections for 2-to-1 meson–meson scattering
European Physical Journal C: Particles and Fields, 2021 We study the processes $$K{\bar{K}} \rightarrow \phi $$ K K ¯ → ϕ , $$\pi D \rightarrow D^*$$ π D → D ∗ , $$\pi {\bar{D}} \rightarrow {\bar{D}}^*$$ π D ¯ → D ¯ ∗ , and the production of $$\psi (3770)$$ ψ ( 3770 ) , $$\psi (4040)$$ ψ ( 4040 ) , $$\psi ...
Wan-Xia Li, Xiao-Ming Xu, H. J. Weber
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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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Complete monotonicity involving some ratios of gamma functions
Journal of Inequalities and Applications, 2017 In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic.
Zhen-Hang Yang, Shen-Zhou Zheng
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