A Double Inequality for the Trigamma Function and Its Applications-Reference-Cited by-同舟云学术

A Double Inequality for the Trigamma Function and Its Applications

Published:2014 Issue: Volume:2014 Page:1-9
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Yang Zhen-Hang¹^ORCID,Chu Yu-Ming¹,Tao Xiao-Jing²

Affiliation:

1. School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China

2. College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Abstract

We prove thatp=1andq=2are the best possible parameters in the interval(0,∞)such that the double inequalityep/x+1-e-p/x/2p<ψ′x+1<eq/x+1-e-q/x/2qholds forx>0. As applications, some new approximation algorithms for the circumference ratioπand Catalan constantG=∑n=0∞-1n/(2n+1)2are given. Here,ψ′is the trigamma function.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/702718.pdf

Reference20 articles.

1. A monotoneity property of the gamma function

2. The best bounds in Gautschi's inequality

3. Sharp bounds for the psi function and harmonic numbers

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