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# Fungrim entry: 9f32fe

$\psi\!\left(z + n\right) = \psi\!\left(z\right) + \sum_{k=0}^{n - 1} \frac{1}{z + k}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}$
TeX:
\psi\!\left(z + n\right) = \psi\!\left(z\right) + \sum_{k=0}^{n - 1} \frac{1}{z + k}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Sum$\sum_{n} f(n)$ Sum
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("9f32fe"),
Formula(Equal(DigammaFunction(Add(z, n)), Add(DigammaFunction(z), Sum(Div(1, Add(z, k)), For(k, 0, Sub(n, 1)))))),
Variables(z, n),
Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(0)), Element(n, 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