Complete monotonicity of a function involving the $p$-psi function and alternative proofs

Abstract

In the paper the authors alternatively prove that the function $x^{\alpha }[\ln \frac{px}{x+p+1}-{\psi }_p(x)]$ is completely monotonic on $(0,\infty )$ if and only if $\alpha \le 1$, where $p\in \mathbb{N}$ and ${\psi }_p(x)$ is the $p$-analogue of the classical psi function $\psi (x)$. This generalizes a known result.

5 pages

References in corpus (1)

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

Cited by in corpus (1)

• A logarithmically completely monotonic function involving the ratio of gamma functions