A double inequality for the trigamma function and its applications
type: Item
instance of: scholarly article
title: A double inequality for the trigamma function and its applications
zbMATH Open document ID: 1474.33012
DOI: 10.1155/2014/702718
author: Zhen-Hang Yang
author: Yu-Ming Chu
author: Xiao-Jing Tao
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We prove that \(p = 1\) and \(q = 2\) are the best possible parameters in the interval \((0, \infty)\) such that the double inequality \(\left(e^{p / \left(x + 1\right)} - e^{- p / x}\right) / 2 p < \psi' \left(x + 1\right) < \left(e^{q / \left(x + 1\right)} - e^{- q / x}\right) / 2 q\) holds for \(x > 0\). As applications, some new approximation algorithms for the circumference ratio \(\pi\) and Catalan constant \(G = \sum_{n = 0}^\infty \left(\left(- 1\right)^n /(2 n + 1)^2\right)\) are given. Here, \(\psi'\) is the trigamma function.
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 7022908
Wikidata QID: Q59040735
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/702718
OpenAlex ID: W2000707474
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description: scientific article; zbMATH DE number 7022908