On a Conjecture of Alzer, Berg, and Koumandos

Abstract

In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ ( x ) denotes the logarithmic derivative of Euler’s gamma function.