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Approximation for the gamma function via the tri-gamma function [PDF]

open access: yesJournal 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]

open access: yesJournal 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

On Gamma Function Inequalities [PDF]

open access: bronzeMathematics of Computation, 1986
We show that certain functions involving quotients of gamma functions are completely monotonic. This leads to inequalities involving gamma functions. We also establish the infinite divisibility of several probability distributions whose Laplace transforms involve quotients of gamma functions.
J. Bustoz, Mourad E. H. Ismail
openalex   +2 more sources

On rational bounds for the gamma function [PDF]

open access: yesJournal of Inequalities and Applications, 2017
In the article, we prove that the double inequality [Formula: see text] holds for all [Formula: see text], we present the best possible constants λ and μ such that [Formula: see text] for all [Formula: see text], and we find the value of [Formula: see text] in the interval [Formula: see text] such that [Formula: see text] for [Formula: see text] and ...
Wen Zhang   +3 more
openaire   +5 more sources

Gamma-Bazilevič Functions [PDF]

open access: yesMathematics, 2020
For γ ≥ 0 and α ≥ 0 , we introduce the class B 1 γ ( α ) of Gamma–Bazilevič functions defined for z ∈ D by R e z f ′ ( z ) f ( z ) 1 − α z α + z f ″ ( z ) f ′ ( z ) + ( α − 1 ) z f ′ ( z ) f ( z ) − 1 γ z f ′ ( z ) f ( z ) 1 − α z α
Fitri, Sa’adatul, Thomas, Derek K.
openaire   +5 more sources

Some general Gompertz and Gompertz-Makeham life expectancy models

open access: yesAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
Life expectancy models are highly important, as they indicate the populations health. The present models consider several types of factors, and by analyzing them we extend the formulae to new, mixed types in order to create particular representations ...
Drăgan Mihăiţă
doaj   +1 more source

A short note on a extended finite secant series

open access: yesAIMS Mathematics, 2023
In this paper, a summation formula for a general family of a finite secant sum has been extended by making use of a particularly convenient integration contour method.
Robert Reynolds
doaj   +1 more source

On the Nonlinear Integro-Differential Equations

open access: yesFractal and Fractional, 2021
The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces.
Chenkuan Li, Joshua Beaudin
doaj   +1 more source

Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function

open access: yesMathematics, 2021
The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function.
Shilpi Jain   +4 more
doaj   +1 more source

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