Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function
type: Item
instance of: scholarly article
title: Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function
author: Hong-Ping Yin
author: Lingxiong Han
author: Feng Qi
published in: Demonstratio Mathematica
publication date: 2024-08-21T00:00:00Z
review text: Polygamma functions are defined by logarithmic derivatives of the Euler gamma function.\NMany works in the literature are focused on the study and applications of polygamma functions and inequalities involving them. In this paper, the authors find the necessary and sufficient conditions for a function defined by three derivatives of a function involving a trigamma function to be completely monotonic.\NThese results also confirm some previous open questions posed by the third author in [Appl. Anal. Discrete Math. 15, No. 2, 378--392 (2021; Zbl 1499.33012)].
reviewed by: Yinying Kong
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 26D07
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 44A35
zbMATH DE Number: 7899345
zbMATH Keywords: decreasing monotonicity
zbMATH Keywords: complete monotonicity
zbMATH Keywords: completely monotonic function
zbMATH Keywords: trigamma function
zbMATH Keywords: derivative
zbMATH Keywords: ratio
zbMATH Keywords: convolution theorem
zbMATH Keywords: inequality
zbMATH Keywords: monotonicity rule
zbMATH Keywords: Laplace transform
zbMATH Keywords: Bernstein's theorem
zbMATH Keywords: exponential function guess
MaRDI profile type: Publication
cites work: Q3331506
cites work: Q5287501
cites work: Bernstein functions. Theory and applications
cites work: The Laplace transform.
cites work: Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function
cites work: Some properties of several functions involving polygamma functions and originating from the sectional curvature of the beta manifold
cites work: Monotonicity and inequalities for the gamma function
cites work: Table of integrals, series, and products. Translated from the Russian. Translation edited and with a preface by Victor Moll and Daniel Zwillinger
cites work: Q4441514
cites work: Integral representations of bivariate complex geometric mean and their applications
DOI: 10.1515/DEMA-2024-0041
description: scientific article; zbMATH DE number 7899345