Short Remarks on Complete Monotonicity of Some Functions

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 4, 1-14

Abstract: In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1 | β ( m ) ( x ) | and x m − 1 | ψ ( m ) ( x ) | are completely monotonic on ( 0 , ∞ ) for all m ∈ N , m > 2 , where ψ ( x ) denotes the logarithmic derivative of Euler’s gamma function.

Keywords: completely monotonic functions; laplace transform; inequality; Nielsen’s ? -function; polygamma functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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