An application of a moment problem to completely monotonic functions
Abstract
We consider the following question: if a function of the form ∫0∞(t)\, e-xtdt is completely monotonic, is it then 0? It turns out that the question is related to a moment problem. In the end we apply those results to answer some questions concerning complete monotonicity of certain functions raised in F. Qi and R. Agarwal, On complete monotonicity for several classes of functions related to ratios of gamma functions, J. Inequal. Appl. (2019).
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