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Short Remarks on Complete Monotonicity of Some Functions

Faculty of Industrial Technologies in Púchov, Trenčín University of Alexander Dubček in Trenčín, I. Krasku 491/30, 02001 Púchov, Slovakia
Mathematics 2020, 8(4), 537; https://doi.org/10.3390/math8040537
Received: 25 February 2020 / Revised: 22 March 2020 / Accepted: 28 March 2020 / Published: 5 April 2020
(This article belongs to the Special Issue Applications of Inequalities and Function Analysis)
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. View Full-Text
Keywords: completely monotonic functions; laplace transform; inequality; Nielsen’s β-function; polygamma functions completely monotonic functions; laplace transform; inequality; Nielsen’s β-function; polygamma functions
MDPI and ACS Style

Matejíčka, L. Short Remarks on Complete Monotonicity of Some Functions. Mathematics 2020, 8, 537.

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