Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Lower Bound of Sectional Curvature of Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions

Version 1 : Received: 7 November 2020 / Approved: 10 November 2020 / Online: 10 November 2020 (13:26:15 CET)

How to cite: Qi, F. Lower Bound of Sectional Curvature of Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions. Preprints 2020, 2020110315 (doi: 10.20944/preprints202011.0315.v1). Qi, F. Lower Bound of Sectional Curvature of Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions. Preprints 2020, 2020110315 (doi: 10.20944/preprints202011.0315.v1).

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.

Subject Areas

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

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