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Fungrim entry: 1cbe83

ψ(m) ⁣(∞)=lim⁡x→∞ψ ⁣(x)={∞,m=00,m>0\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∈Z≥0m \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
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Infinity∞\infty Positive infinity
RealLimitlim⁡x→af(x)\lim_{x \to a} f(x) Limiting value, real variable
ZZGreaterEqualZ≥n\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