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

Abstract

In the present paper, we give two new proofs for the necessary and sufficient condition $\alpha \le 1$ such that the function $x^{\alpha }[\ln x-\psi (x)]$ is completely monotonic on $(0,\infty )$.

6 pages

References in corpus (1)

• Some logarithmically completely monotonic functions related to the gamma function

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