• 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}
}
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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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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