Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2010; 47(1): 103-111

Printed January 1, 2010

https://doi.org/10.4134/BKMS.2010.47.1.103

Copyright © The Korean Mathematical Society.

Two new proofs of the complete monotonicity of a function involving the psi function

Bai-Ni Guo and Feng Qi

Henan Polytechnic University and Tianjin Polytechnic University

Abstract

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In the present paper, we give two new proofs for the necessary and sufficient condition $\alpha\le1$ such that the function $x^\alpha[\ln x-\psi(x)]$ is completely monotonic on $(0,\infty)$.

Keywords: new proof, completely monotonic function, psi function, inequality

MSC numbers: Primary 33B15, 65R10; Secondary 26A48, 26A51

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