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

Stieltjes constants