Some logarithmically completely monotonic functions related to the gamma function
Abstract
In this article, logarithmically complete monotonicity properties of some functions such as 1[(x+1)]1/x, [(x+α+1)]1/(x+α)[(x+1)]1/x, [(x+1)]1/x(x+1)α and [(x+1)]1/xxα defined in (-1,∞) or (0,∞) for given real number α∈ are obtained, some known results are recovered, extended and generalized. Moreover, some basic properties of the logarithmically completely monotonic functions are established.
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