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Fungrim entry: d10029

Symbol: StieltjesGamma γn ⁣(a)\gamma_{n}\!\left(a\right) Stieltjes constant
StieltjesGamma(n), rendered as γn\gamma_{n}, represents the Stieltjes constant of index nn.
StieltjesGamma(n, a), rendered as γn ⁣(a)\gamma_{n}\!\left(a\right), represents the generalized Stieltjes constant of index nn with parameter aa.
Domain Codomain
nZ0n \in \mathbb{Z}_{\ge 0} γnR\gamma_{n} \in \mathbb{R}
nZ0andaCanda{0,1,}n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, a \notin \{0, -1, \ldots\} γn ⁣(a)C\gamma_{n}\!\left(a\right) \in \mathbb{C}
Table data: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
StieltjesGammaγn ⁣(a)\gamma_{n}\!\left(a\right) Stieltjes constant
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
RRR\mathbb{R} Real numbers
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\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)))))

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

2019-09-16 21:17:18.797188 UTC