Completely and logarithmically completely monotone functions
Abstract
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory. Furthermore, we use the results obtained to investigate the monotonicity properties of some specific functions related to the Gamma function. Finally, we formulate an open problem related to the psi function.
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