A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function

Abstract

In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the function $(1+\frac{\alpha }{x}{)}^{x+\beta }$ are proved, where $\alpha$ and $\beta$ are given real parameters, a new proof for the inclusion that a logarithmically completely monotonic function is also completely monotonic is given, and an open problem is posed.

8 pages

References in corpus (1)

• Some logarithmically completely monotonic functions related to the gamma function

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