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Fungrim entry: 1e47db

∑k=1nψ ⁣(k)=n(ψ ⁣(n+1)−1)\sum_{k=1}^{n} \psi\!\left(k\right) = n \left(\psi\!\left(n + 1\right) - 1\right)
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\sum_{k=1}^{n} \psi\!\left(k\right) = n \left(\psi\!\left(n + 1\right) - 1\right)

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Sum∑nf(n)\sum_{n} f(n) Sum
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("1e47db"),
    Formula(Equal(Sum(DigammaFunction(k), For(k, 1, n)), Mul(n, Sub(DigammaFunction(Add(n, 1)), 1)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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