A Note on an Open Problem
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An, Miao-Qing (2009) A Note on an Open Problem. Research report collection, 12 (2).
Abstract
The function (Γ(x+1)¹/x)/((x+β)α) is logarithmically completely monotonic on (0,∞) for α ≥ 1 and 0 ≤ β ≤ 1, and is logarithmically completely monotonic in (−1, 0) for 0 < α ≤ (2β)/(1+2β)� and β > 1. This gives an answer to an open problem proposed by Feng Qi.
| Item type | Article |
| URI | https://vuir.vu.edu.au/id/eprint/18953 |
| Subjects | Historical > FOR Classification > 0101 Pure Mathematics Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA) |
| Keywords | gamma function, psi function, polygamma function, complete monotonicity, logarithmically complete monotonicity |
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