# Fungrim entry: 687b4d

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

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; 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
Pow${a}^{b}$ Power
Log$\log(z)$ Natural logarithm
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("687b4d"),
Formula(Equal(StieltjesGamma(n, Add(a, 1)), Sub(StieltjesGamma(n, a), Div(Pow(Log(a), n), a)))),
Variables(n, a),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(a, CC), NotElement(a, ZZLessEqual(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