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Bernoulli number
(Q694114)
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From Wikidata
rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯
Bernoulli numbers
edit
Language
Label
Description
Also known as
default for all languages
No label defined
–
English
Bernoulli number
rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯
Bernoulli numbers
Statements
instance of
sequence of real numbers
0 references
mathematical concept
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subclass of
rational number
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image
JakobBernoulliSummaePotestatum.png
576 × 732; 19 KB
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Seki Kowa Katsuyo Sampo Bernoulli numbers.png
1,614 × 2,124; 5.41 MB
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Bernoulli numbers graphs.svg
512 × 512; 9 KB
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Bernoulli numbers logarithmic growth.png
480 × 400; 14 KB
reason for preferred rank
editorial choice
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named after
Jacob Bernoulli
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discoverer or inventor
Jacob Bernoulli
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Takakazu Seki
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time of discovery or invention
1710s
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defining formula
B
n
=
{
−
1
n
+
1
∑
k
=
0
n
−
1
(
n
+
1
k
)
B
k
n
>
0
1
n
=
0
{\displaystyle \mathrm {B} _{n}={\begin{cases}-{\frac {1}{n+1}}\sum _{k=0}^{n-1}{\binom {n+1}{k}}\mathrm {B} _{k}&n>0\\1&n=0\end{cases}}}
1 reference
stated in
ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
section, verse, paragraph, or clause
2-11.5
in defining formula
B
n
{\displaystyle \mathrm {B} _{n}}
symbol represents
Bernoulli number
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(
n
k
)
{\displaystyle {\binom {n}{k}}}
symbol represents
binomial coefficient
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described by source
ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
section, verse, paragraph, or clause
2-11.5
subject named as
Bernoulli numbers
0 references
maintained by WikiProject
WikiProject Mathematics
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Stack Exchange tag
https://stackoverflow.com/tags/bernoulli-numbers
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Commons category
Bernoulli numbers
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Identifiers
Bibliothèque nationale de France ID
12286125h
1 reference
stated in
Nuovo soggettario
reference URL
http://thes.bncf.firenze.sbn.it/termine.php?id=37195&menuR=2&menuS=2
retrieved
3 January 2018
GND ID
4276648-5
1 reference
stated in
Library of Congress Subject Headings
Library of Congress authority ID
sh85013375
retrieved
3 January 2018
FAST ID
830779
1 reference
stated in
Faceted Application of Subject Terminology
retrieved
3 January 2018
J9U ID
987007283266005171
1 reference
stated in
National Library of Israel
Library of Congress authority ID
sh85013375
1 reference
stated in
Nuovo soggettario
reference URL
http://thes.bncf.firenze.sbn.it/termine.php?id=37195&menuR=2&menuS=2
retrieved
3 January 2018
NL CR AUT ID
ph982960
subject named as
Bernoulliho čísla
0 references
BNCF Thesaurus ID
37195
1 reference
stated in
Nuovo soggettario
Freebase ID
/m/01klw
1 reference
stated in
Freebase Data Dumps
publication date
28 October 2013
Gran Enciclopèdia Catalana ID
nombres-de-bernoulli
0 references
Gran Enciclopèdia Catalana ID (former scheme)
0009534
0 references
Lexikon der Mathematik entry ID
1032
subject named as
Bernoullische Zahlen
0 references
LMFDB knowl ID
af.bernoulli_numbers
0 references
MathWorld ID
BernoulliNumber
subject named as
Bernoulli Number
1 reference
imported from Wikimedia project
English Wikipedia
Microsoft Academic ID
129960964
0 references
nLab ID
Bernoulli number
0 references
OEIS ID
A027642
applies to part
denominator
0 references
A027641
applies to part
numerator
0 references
OpenAlex ID
C129960964
1 reference
stated in
OpenAlex
retrieved
26 January 2022
reference URL
https://docs.openalex.org/download-snapshot/snapshot-data-format
ProofWiki ID
Definition:Bernoulli_Numbers
0 references
Rosetta Code page ID
Bernoulli_numbers
0 references
ScienceDirect topic ID
mathematics/bernoulli-number
0 references
computer-science/bernoulli-number
0 references
Treccani's Enciclopedia della Matematica ID
numeri-di-bernoulli
subject named as
Bernoulli, numeri di
publication date
2013
0 references
Sitelinks
Wikipedia
(39 entries)
edit
arwiki
عدد برنولي
azwiki
Bernulli ədədləri
bgwiki
Числа на Бернули
cawiki
Nombres de Bernoulli
cswiki
Bernoulliho číslo
dewiki
Bernoulli-Zahl
elwiki
Αριθμός Μπερνούλι
enwiki
Bernoulli number
eswiki
Número de Bernoulli
euwiki
Bernoulliren zenbaki
fawiki
عدد برنولی
fiwiki
Bernoullin luku
frwiki
Nombre de Bernoulli
glwiki
Número de Bernoulli
hewiki
מספרי ברנולי
hiwiki
बर्नूली संख्या
huwiki
Bernoulli-számok
idwiki
Bilangan Bernoulli
itwiki
Numeri di Bernoulli
jawiki
ベルヌーイ数
kkwiki
Бернулли сандары
kowiki
베르누이 수
lvwiki
Bernulli skaitlis
nlwiki
Bernoulligetal
nowiki
Bernoulli-tall
plwiki
Liczby Bernoulliego
ptwiki
Números de Bernoulli
ruwiki
Числа Бернулли
simplewiki
Bernoulli number
slwiki
Bernoullijevo število
srwiki
Бернулијеви бројеви
svwiki
Bernoullital
thwiki
จำนวนแบร์นูลลี
trwiki
Bernoulli sayısı
ukwiki
Числа Бернуллі
urwiki
برنولی عدد
uzwiki
Bernoulli sonlari
zh_yuewiki
伯努利數
zhwiki
伯努利数
Wikibooks
(0 entries)
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Wikinews
(0 entries)
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Wikiquote
(0 entries)
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Wikisource
(0 entries)
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Wikiversity
(0 entries)
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Wikivoyage
(0 entries)
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Wiktionary
(0 entries)
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Multilingual sites
(1 entry)
edit
commonswiki
Category:Bernoulli numbers
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