Results 1 to 10 of about 607,360 (246)

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
doaj   +5 more sources

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
doaj   +2 more sources

The Minimum in the Gamma Function [PDF]

Nature, 1935
IT is well known that the gamma function “(z) for real and positive values of z has a minimum between z = 1.46 and 1.47. In a number of texts on the theory of functions it is stated that the minimum occurs at z = 1.4616321 and that the corresponding value of “(z) is 0.8856032 Only one text that we have examined, namely Joseph Edwards's monumental work ...
Deming, W. Edwards, Colcord, Clarence G.
openaire   +2 more sources

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, Shaher Momani, Praveen Agarwal, Michael Th. Rassias   +3 more
doaj   +1 more source

The gamma function via interpolation [PDF]

Numerical Algorithms, 2021
19 ...
openaire   +2 more sources

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
doaj   +1 more source

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, Benachour Mustapha, Benachour Nadjia   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Certain Recurrence Relations of Two Parametric Mittag-Leffler Function and Their Application in Fractional Calculus

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, Shailesh Jaloree, Junesang Choi   +2 more
doaj   +1 more source