We prove that and are the best possible parameters in the interval such that the double inequality holds for . As applications, some new approximation algorithms for the circumference ratio and Catalan constant are given. Here, is the trigamma function.
"A Double Inequality for the Trigamma Function and Its Applications." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/702718