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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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An Extension of Beta Function by Using Wiman’s Function
Axioms, 2021 The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman.
Rahul Goyal +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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Prediction of Fatigue Cracks Using Gamma Function
Fatigue of Aircraft Structures, 2023 In the present study it has been endeavored to estimate the fatigue crack propagation in V-notch Charpy specimens of 2024 T351 Al-alloy. For this purpose, a new application of fatigue crack growth (FCG) is developed based on the “Gamma function ...
Moussouni Abdelfetah +2 more
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Monotonicity of the incomplete gamma function with applications
Journal of Inequalities and Applications, 2016 In the article, we discuss the monotonicity properties of the function x → ( 1 − e − a x p ) 1 / p / ∫ 0 x e − t p d t $x\rightarrow (1-e^{-ax^{p}} )^{1/p}/\int_{0}^{x}e^{-t^{p}}\,dt$ for a , p > 0 $a, p>0$ with p ≠ 1 $p\neq1$ on ( 0 , ∞ ) $(0, \infty ...
Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu
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New Applications of the Bernardi Integral Operator
Mathematics, 2020 Let A ( p , n ) be the class of f ( z ) which are analytic p-valent functions in the closed unit disk U ¯ = z ∈ C : z ≤ 1 . The expression B − m − λ f ( z ) is defined by using fractional integrals of order λ
Shigeyoshi Owa, H. Özlem Güney
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Fractal and Fractional, 2021 The purpose of this paper is to develop some new recurrence relations for the two parametric Mittag-Leffler function. Then, we consider some applications of those recurrence relations.
Dheerandra Shanker Sachan +2 more
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Multiple Gamma Functions and Multiple $q$-Gamma Functions
Publications of the Research Institute for Mathematical Sciences, 1997 We give an asymptotic expansion ( the higher Stirling formula ) and an infinite product representation ( the Weierstrass canonical product representation ) of the Vigneras multiple gamma functions by considering the classical limit of the multiple
Ueno, Kimio, Nishizawa, Michitomo
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Integral Representations of a Generalized Linear Hermite Functional
Mathematics, 2023 In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
Roberto S. Costas-Santos
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