Results 1 to 10 of about 12,298,354 (363)
Approximation for the gamma function via the tri-gamma function [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series.
Xu You, Xiaocui Li
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Note on the Degenerate Gamma Function [PDF]
Russian Journal of Mathematical Physics, 2020 Recently, the degenerate gamma functions were introduced as a degenerate version of the usual gamma function. In this paper, we investigate several properties of these functions. Namely, we obtain an analytic continuation as a meromorphic function on the
Kim T, Kim D.
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Regularized Integral Representations of the Reciprocal Gamma Function [PDF]
Fractal and Fractional, 2019 This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived.
Dimiter Prodanov
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Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function. [PDF]
J Inequal Appl, 2018 In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev’s inequality for synchronous (or asynchronous, respectively ...
Nisar KS +4 more
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On rational bounds for the gamma function. [PDF]
J Inequal Appl, 2017 In the article, we prove that the double inequality x2+p0x+p0(x^{2}+1/\gamma)/(x+1/\gamma)$\end{document} for x∈(0,x∗)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
Yang ZH, Qian WM, Chu YM, Zhang W.
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An accurate approximation formula for gamma function. [PDF]
J Inequal Appl, 2018 In this paper, we present a very accurate approximation for the gamma function: Γ(x+1)∼2πx(xe)x(xsinh1x)x/2exp(73241x3(35x2+33))=W2(x)$$ \Gamma( x+1 ) \thicksim\sqrt{2\pi x} \biggl( \frac{x}{e} \biggr) ^{x} \biggl( x\sinh\frac{1}{x} \biggr) ^{x/2}\exp \
Yang ZH, Tian JF.
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Padé approximant related to asymptotics for the gamma function [PDF]
Journal of Inequalities and Applications, 2017 Based on the Padé approximation method, we determine the coefficients a j $a_{j}$ and b j $b_{j}$ ( 1 ≤ j ≤ k $1\leq j\leq k$ ) such that Γ ( x + 1 ) 2 π x ( x / e ) x = x k + a 1 x k − 1 + ⋯ + a k x k + b 1 x k − 1 + ⋯ + b k + O ( 1 x 2 k + 1 ) , x → ∞ ,
Xin Li, Chao-Ping Chen
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On Complex Gamma-Function Integrals [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 It was observed recently that relations between matrix elements of certain operators in the ${\rm SL}(2,\mathbb R)$ spin chain models take the form of multidimensional integrals derived by R.A. Gustafson.
S. Derkachov, A. Manashov
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Results in Mathematics, 2017 We improve the upper bound of the following inequalities for the gamma function $$\Gamma $$Γ due to H. Alzer and the author. $$\begin{aligned} \exp \left( -\frac{1}{2}\psi (x+1/3)\right)
Necdet Batır
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Monotonicity and inequalities for the gamma function
Journal of Inequalities and Applications, 2017 In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x ↦ 1 24 x ( ln Γ ( x + 1 / 2 ) − x ln x + x − ln 2 π ) + 1 − 120 7 x 2 $$ x\mapsto \frac{1}{24x ( \ln \Gamma ( x+1/2 ) -x\ln x+x- \ln \sqrt{
Zhen-Hang Yang, Jing-Feng Tian
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