Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function

Chao-Ping Chen; Richard B. Paris

doi:10.1016/j.amc.2014.11.010

Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function

Chao-Ping Chen, Richard B. Paris

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Abstract

In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2).

Original language	English
Pages (from-to)	514-529
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	250
Early online date	22 Nov 2014
DOIs	https://doi.org/10.1016/j.amc.2014.11.010
Publication status	Published - 1 Jan 2015

Keywords

Gamma function
Psi function
Polygamma functions
Asymptotic expansion
Completely monotonic functions
Inequality

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10.1016/j.amc.2014.11.010

Paris_Inequalities,AsymptoticExpansionsAndCompletelyMonotonicFunctionsRelatedToTheGammaFunction_Author_2014Accepted author manuscript, 335 KBLicence: CC BY-NC-ND

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title = "Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function",

abstract = "In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2).",

author = "Chao-Ping Chen and Paris, \{Richard B.\}",

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AU - Paris, Richard B.

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N2 - In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2).

AB - In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2).

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DO - 10.1016/j.amc.2014.11.010

M3 - Article

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VL - 250

SP - 514

EP - 529

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

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Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function

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