Monotonicity and convexity of the function x√Г(x+1)/ (x+α}√Г(x+α+1)
Download
Download
DownloadExport
Qi, Feng and Guo, Bai-Ni (2003) Monotonicity and convexity of the function x√Г(x+1)/ (x+α}√Г(x+α+1). RGMIA research report collection, 6 (4).
Abstract
For α>0 a real number, the function x√Γ(x+1)/(x+α)√Γ(x+α+1) is increasing with x∈(x0,∞) and logarithmically concave with x∈[1,∞), wherex0∈(0,1) is a constant. Moreover, some monotonicity and convexity results and inequalities of functions involving the gamma function and polygamma functions are obtained as corollaries and by-products.
| Item type | Article |
| URI | https://vuir.vu.edu.au/id/eprint/17868 |
| Subjects | Historical > FOR Classification > 0102 Applied Mathematics Historical > FOR Classification > 0103 Numerical and Computational Mathematics Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA) |
| Keywords | gamma function, polygamma function, monotonicity, convexity, mean value, inequality, ratio |
| Download/View statistics | View download statistics for this item |
CORE (COnnecting REpositories)