# Fungrim entry: 1cbe83

$\psi^{(m)}\!\left(\infty\right) = \lim_{x \to \infty} \psi\!\left(x\right) = \begin{cases} \infty, & m = 0\\0, & m > 0\\ \end{cases}$
Assumptions:$m \in \mathbb{Z}_{\ge 0}$
TeX:
\psi^{(m)}\!\left(\infty\right) = \lim_{x \to \infty} \psi\!\left(x\right) = \begin{cases} \infty, & m = 0\\0, & m > 0\\ \end{cases}

m \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Infinity$\infty$ Positive infinity
RealLimit$\lim_{x \to a} f(x)$ Limiting value, real variable
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("1cbe83"),
Formula(Equal(DigammaFunction(Infinity, m), RealLimit(DigammaFunction(x), For(x, Infinity)), Cases(Tuple(Infinity, Equal(m, 0)), Tuple(0, Greater(m, 0))))),
Variables(m),
Assumptions(Element(m, ZZGreaterEqual(0))))

## 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