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Fungrim entry: dce62c

lim⁡x→0+ψ ⁣(x)=(−1)m+1∞\lim_{x \to {0}^{+}} \psi\!\left(x\right) = {\left(-1\right)}^{m + 1} \infty
Assumptions:m∈Z≥0m \in \mathbb{Z}_{\ge 0}
TeX:
\lim_{x \to {0}^{+}} \psi\!\left(x\right) = {\left(-1\right)}^{m + 1} \infty

m \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
RightLimitlim⁡x→a+f(x)\lim_{x \to {a}^{+}} f(x) Limiting value, from the right
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Powab{a}^{b} Power
Infinity∞\infty Positive infinity
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("dce62c"),
    Formula(Equal(RightLimit(DigammaFunction(x), For(x, 0)), Mul(Pow(-1, Add(m, 1)), Infinity))),
    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