Some inequalities for the trigamma function in terms of the digamma function

摘要

In the paper, the authors establish three kinds of double inequalities forthe trigamma function in terms of the exponential function to powers of thedigamma function. These newly established inequalities extend some knownresults. The method in the paper utilizes some facts from the asymptotic theoryand is a natural way to solve problems for approximating some quantities forlarge values of the variable.