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

Stieltjes constants