Fungrim entry: 86333d

\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C}} \psi^{(m)}\!\left(z\right) = \{0, -1, \ldots\}

Assumptions:

m \in \mathbb{Z}_{\ge 0}

TeX:

\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C}} \psi^{(m)}\!\left(z\right) = \{0, -1, \ldots\}

m \in \mathbb{Z}_{\ge 0}

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
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("86333d"),
    Formula(Equal(Poles(DigammaFunction(z, m), ForElement(z, CC)), ZZLessEqual(0))),
    Variables(m),
    Assumptions(Element(m, ZZGreaterEqual(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