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Approximation for the gamma function via the tri-gamma function [PDF]
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]
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 Gamma Function Inequalities [PDF]
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
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On rational bounds for the gamma function [PDF]
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
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Gamma-Bazilevič Functions [PDF]
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.
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Some general Gompertz and Gompertz-Makeham life expectancy models
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
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A short note on a extended finite secant series
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
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On the Nonlinear Integro-Differential Equations
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
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Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
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
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