Submitted:
07 November 2020
Posted:
10 November 2020
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Abstract
In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.
Keywords:
necessary and sufficient condition
; complete monotonicity
; monotonicity
; inequality
; polygamma function
; lower bound
; sectional curvature
; manifold
; beta distribution
; convolution theorem for the Laplace transforms and analytic techniques
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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