On a Conjecture of Alzer, Berg, and Koumandos

Ladislav Matejíčka
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Ladislav Matejíčka: Faculty of Industrial Technologies in Púchov, Trenčín University of Alexander Dubček in Trenčín, I. Krasku 491/30, 02001 Púchov, Slovakia

Mathematics, 2020, vol. 8, issue 6, 1-9

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.

Keywords: completely monotonic functions; inequality; polygamma function; digamma function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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