• Corpus ID: 12427391

# Monotonicity Results For The Gamma Function

```@article{Chen2002MonotonicityRF,
title={Monotonicity Results For The Gamma Function},
author={Chao Chen and Feng Qi (祁锋)},
journal={Journal of Inequalities in Pure \& Applied Mathematics},
year={2002},
volume={4}
}```
• Published 2002
• Mathematics
• Journal of Inequalities in Pure & Applied Mathematics
The function 1/x x+1 is strictly decreasing on[1,∞), the function [Γ(x+1)]1/x √ x is strictly increasing on[2,∞), and the function 1/x √ x+1 is strictly increasing on[1,∞), respectively. From these, some inequalities, for example, the Minc-Sathre inequality, are deduced, and two open problems posed by the second author are solved partially.
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## References

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In the article, using the monotonicity and inequalities of the generalized weighted mean values with two parameters, we prove that the functions [ Γ(s)/Γ(r) ]1/(s−r) , [ Γ(s, x)/Γ(r, x) ]1/(s−r) and
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Let f be an increasing and convex (concave) function on [0, 1) and φ a positive increasing concave function on [0,∞) such that φ(0) = 0 and the sequence { φ(i+1) ( φ(i+1) φ(i) − 1 )} i∈N decreases (
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In the article, many inequalities of the integrals f 00 z e'dt, e"dt, j for p > 0, which are related to the incomplete gamma function, are established. The approach used in the paper could yield more
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• 2003
In this article, using Stirling’s formula, the series-expansion of digamma functions and other techniques, some inequalities and monotonicity concerning the ratio of gamma functions are obtained,