A Double Inequality for the Trigamma Function and Its Applications

Abstract EN

We prove that p=1 and q=2 are the best possibleparameters in the interval (0,∞) such that the double inequality ep/x+1-e-p/x/2p<ψ′x+10.

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.