# Fungrim entry: 5a3c4a

${\left(-1\right)}^{m + 1} \psi^{(m)}\!\left(x\right) > \frac{\left(m - 1\right)!}{{x}^{m}} + \frac{m !}{2 {x}^{m + 1}}$
Assumptions:$m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)$
TeX:
{\left(-1\right)}^{m + 1} \psi^{(m)}\!\left(x\right) > \frac{\left(m - 1\right)!}{{x}^{m}} + \frac{m !}{2 {x}^{m + 1}}

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Factorial$n !$ Factorial
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("5a3c4a"),
Variables(m, x),
Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(x, OpenInterval(0, Infinity)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC