Fungrim entry: 11dfd2

\psi\!\left(z + 1\right) = \psi\!\left(z\right) + \frac{1}{z}

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

TeX:

\psi\!\left(z + 1\right) = \psi\!\left(z\right) + \frac{1}{z}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("11dfd2"),
    Formula(Equal(DigammaFunction(Add(z, 1)), Add(DigammaFunction(z), Div(1, z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(0)))))

Topics using this entry

Digamma function

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