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# Fungrim entry: d10029

Symbol: StieltjesGamma $\gamma_{n}\!\left(a\right)$ Stieltjes constant
StieltjesGamma(n), rendered as $\gamma_{n}$, represents the Stieltjes constant of index $n$.
StieltjesGamma(n, a), rendered as $\gamma_{n}\!\left(a\right)$, represents the generalized Stieltjes constant of index $n$ with parameter $a$.
Domain Codomain
$n \in \mathbb{Z}_{\ge 0}$ $\gamma_{n} \in \mathbb{R}$
$n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, a \notin \{0, -1, \ldots\}$ $\gamma_{n}\!\left(a\right) \in \mathbb{C}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \implies \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
StieltjesGamma$\gamma_{n}\!\left(a\right)$ Stieltjes constant
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
RR$\mathbb{R}$ Real numbers
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("d10029"),
SymbolDefinition(StieltjesGamma, StieltjesGamma(n, a), "Stieltjes constant"),
Description(SourceForm(StieltjesGamma(n)), ", rendered as", StieltjesGamma(n), ", represents the Stieltjes constant of index", n, "."),
Description(SourceForm(StieltjesGamma(n, a)), ", rendered as", StieltjesGamma(n, a), ", represents the generalized Stieltjes constant of index", n, " with parameter", a, "."),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(n, ZZGreaterEqual(0)), Element(StieltjesGamma(n), RR)), Tuple(And(Element(n, ZZGreaterEqual(0)), Element(a, CC), NotElement(a, ZZLessEqual(0))), Element(StieltjesGamma(n, a), CC)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC