Short Remarks on Complete Monotonicity of Some Functions

Ladislav Matejíčka

doi:10.3390/math8040537

journal article Open Access Apr 05, 2020

Short Remarks on Complete Monotonicity of Some Functions

Ladislav Matejíčka

Mathematics Vol. 8 No. 4 pp. 537 · MDPI AG

View at Publisher Save 10.3390/math8040537

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.

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Ladislav Matejíčka

Mathematics 10.3390/math8040537

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Short Remarks on Complete Monotonicity of Some Functions

Ladislav Matejíčka · 2020

Mathematics

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Details

Published: Apr 05, 2020
Vol/Issue: 8(4)
Pages: 537
License: View

Authors

L

Ladislav Matejíčka

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

Cite This Article

Ladislav Matejíčka (2020). Short Remarks on Complete Monotonicity of Some Functions. Mathematics, 8(4), 537. https://doi.org/10.3390/math8040537

Short Remarks on Complete Monotonicity of Some Functions

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