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Fungrim entry: 687b4d

γn ⁣(a+1)=γn ⁣(a)logn ⁣(a)a\gamma_{n}\!\left(a + 1\right) = \gamma_{n}\!\left(a\right) - \frac{\log^{n}\!\left(a\right)}{a}
Assumptions:nZ0  and  aC  and  a{0,1,}n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \notin \{0, -1, \ldots\}
\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\}
Fungrim symbol Notation Short description
StieltjesGammaγn ⁣(a)\gamma_{n}\!\left(a\right) Stieltjes constant
Powab{a}^{b} Power
Loglog(z)\log(z) Natural logarithm
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    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)))))

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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