# Fungrim entry: d4bdf8

$x \in \left(-n, x_{n}\right) \;\implies\; \psi\!\left(x\right) \in \left(-\infty, 0\right)$
Assumptions:$n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}$
TeX:
x \in \left(-n, x_{n}\right) \;\implies\; \psi\!\left(x\right) \in \left(-\infty, 0\right)

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
OpenInterval$\left(a, b\right)$ Open interval
DigammaFunctionZero$x_{n}$ Zero of the digamma function
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Infinity$\infty$ Positive infinity
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("d4bdf8"),
Formula(Implies(Element(x, OpenInterval(Neg(n), DigammaFunctionZero(n))), Element(DigammaFunction(x), OpenInterval(Neg(Infinity), 0)))),
Variables(n, x),
Assumptions(And(Element(n, 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