Bernoulli numbers

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-11.5

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https://metanorma.github.io/isq-smart/math/part-2-11/t2-11.5
urn:iso:std:iso:80000:-2:ed-2:en:item:2-11.5

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-11.5

IEC

urn:iec:std:iec:80000-2:2019:::item:2-11.5

Designations

ENBernoulli numbers

FRnombres de Bernoulli

Symbol

B_{n}

Notation systems

AsciiMath

"B"_n

LaTeX

\text{B}_{n}

Definition

Bernoulli numbers

nombres de Bernoulli

$B_{n} = - \frac{1}{n + 1} \sum_{k = 0}^{n - 1} (\begin{matrix} n + 1 \\ k \end{matrix}) B_{k}$

(for $n > 0$ )

$B_{0} = 1$

$B_{1} = - 1 / 2$ , $B_{2 n + 3} = 0$

$B_{n} = - \frac{1}{n + 1} \sum_{k = 0}^{n - 1} (\begin{matrix} n + 1 \\ k \end{matrix}) B_{k}$

(pour $n$ > 0)

$B_{0} = 1$

$B_{1} = - 1 / 2$ , $B_{2 n + 3} = 0$

A mathematical concept as defined in ISO/IEC 80000 Part 2.

isq:t2-11.5

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-11.5
skosxl:prefLabel	"Bernoulli numbers"@en
skosxl:altLabel	""B"_n"@en
skos:definition	Bernoulli numbers
skos:note	stem:["B"_n = -1/(n+1) sum_(k=0)^(n-1) ((n+1),(k)) "B"_k] (for stem:[n > 0]) stem:["B"_0 = 1] stem:["B"_1 = -1//2], s…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-11