# Fungrim entry: 0e5d90

$\left(m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \text{ odd} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \left(0, \infty\right)$
Assumptions:$m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}$
TeX:
\left(m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \text{ odd} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \left(0, \infty\right)

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
RR$\mathbb{R}$ Real numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
DigammaFunction$\psi\!\left(z\right)$ Digamma function
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("0e5d90"),
Formula(Implies(And(Element(m, ZZGreaterEqual(1)), Odd(m), Element(x, SetMinus(RR, ZZLessEqual(0)))), Element(DigammaFunction(x, m), OpenInterval(0, Infinity)))),
Variables(x, m),
Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(x, RR))))

## 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