Notes on three conjectures involving the digamma and generalized digamma functions

Abstract

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

• Digamma function
• ( p , k ) $(p, k)$ -digamma function
• Complete monotonicity
• Monotonicity
• Inequalities