Open Access
2014 A Double Inequality for the Trigamma Function and Its Applications
Zhen-Hang Yang, Yu-Ming Chu, Xiao-Jing Tao
Abstr. Appl. Anal. 2014: 1-9 (2014). DOI: 10.1155/2014/702718


We prove that p=1 and q=2 are the best possible parameters in the interval (0,) such that the double inequality ep/x+1-e-p/x/2p<ψx+1<eq/x+1-e-q/x/2q holds for x>0. As applications, some new approximation algorithms for the circumference ratio π and Catalan constant G=n=0-1n/(2n+1)2 are given. Here, ψ is the trigamma function.


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Zhen-Hang Yang. Yu-Ming Chu. Xiao-Jing Tao. "A Double Inequality for the Trigamma Function and Its Applications." Abstr. Appl. Anal. 2014 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022908
MathSciNet: MR3240557
Digital Object Identifier: 10.1155/2014/702718

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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