Fungrim entry: b6808d

\gamma_{0}\!\left(a\right) = -\psi\!\left(a\right)

Assumptions:

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

TeX:

\gamma_{0}\!\left(a\right) = -\psi\!\left(a\right)

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

Definitions:

Fungrim symbol	Notation	Short description
`StieltjesGamma`	$\gamma_{n}\!\left(a\right)$	Stieltjes constant
`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("b6808d"),
    Formula(Equal(StieltjesGamma(0, a), Neg(DigammaFunction(a)))),
    Variables(a),
    Assumptions(And(Element(a, CC), NotElement(a, ZZLessEqual(0)))))

Topics using this entry

Stieltjes constants

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