# TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION

• Guo, Bai-Ni ;
• Qi, Feng
• Published : 2010.01.31
• 227 8

#### Abstract

In the present paper, we give two new proofs for the necessary and sufficient condition $\alpha\leq1$ such that the function $x^{\alpha}[lnx-\psi(x)]$ is completely monotonic on (0,$\infty$).

#### Keywords

new proof;completely monotonic function;psi function;inequality

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