Notes on three conjectures involving the digamma and generalized digamma functions

Abstract

In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function.

Keywords: ( p , k ) -digamma function; Complete monotonicity; Digamma function; Inequalities; Monotonicity.