Abstract and Applied Analysis

A Double Inequality for the Trigamma Function and Its Applications

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

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Abstract

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

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 702718, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277112

Digital Object Identifier
doi:10.1155/2014/702718

Mathematical Reviews number (MathSciNet)
MR3240557

Zentralblatt MATH identifier
07022908

Citation

Yang, Zhen-Hang; Chu, Yu-Ming; Tao, Xiao-Jing. A Double Inequality for the Trigamma Function and Its Applications. Abstr. Appl. Anal. 2014 (2014), Article ID 702718, 9 pages. doi:10.1155/2014/702718. https://projecteuclid.org/euclid.aaa/1412277112


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