A Double Inequality for the Trigamma Function and Its Applications

Zhen-Hang Yang, Yu-Ming Chu and Xiao-Jing Tao

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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 0. As applications, some new approximation algorithms for the circumference ratio π and Catalan constant G=∑n=0∞-1n/(21n+) 2 are given. Here, ψ′ is the trigamma function.

Date: 2014
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https://doi.org/10.1155/2014/702718

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:702718

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