Two new proofs of the complete monotonicity of a function involving the psi function
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 103-111
Printed January 1, 2010
Bai-Ni Guo and Feng Qi
Henan Polytechnic University and Tianjin Polytechnic University
Abstract : 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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