Results 11 to 20 of about 6,224,839 (270)
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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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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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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Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function [PDF]
Results in Mathematics, 2015 6 ...
Cristinel Mortici, Feng Qi
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Regularized Integral Representations of the Reciprocal Gamma Function
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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Estimating gamma function by digamma function
Mathematical and Computer Modelling, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cristinel Mortici
exaly +2 more sources
Some Monotonicity Properties of the q-Gamma Function [PDF]
, 2005 We prove some properties of completely monotonic functions and apply them to obtain new results on gamma and q-gamma ...
Gao, Peng
core +6 more sources
A Complete Monotonicity of the Gamma Function [PDF]
, 2004 The function 1/x ln Γ(x+1)−ln x+1 is strictly completely monotonic on (0,∞)
Qi, Feng, Chen, Chao-Ping
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Three Classes of Logarithmically Completely Monotonic Functions Involving Gamma and Psi Functions [PDF]
, 2006 By a simple approach, two classes of functions involving Euler’s gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi function is showed ...
Qi, Feng
core +6 more sources
Experimental Measurements and Computer Simulation of Fission Product Gamma-Ray Spectra [PDF]
, 1997 Airborne gamma ray spectrometry using high volume scintillation detectors, optionally in conjunction with Ge detectors, has potential for making rapid environmental measurements in response to nuclear accidents. An experimental investigation and computer
Sanderson, D.C.W. +4 more
core +8 more sources