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.