|
gptkbp:instanceOf
|
integer sequence
|
|
gptkbp:application
|
gptkb:topology
gptkb:K-theory
modular forms
numerical analysis
finite differences
series expansions
calculation of sums of integer powers
special values of the Riemann zeta function
|
|
gptkbp:B_1
|
-1/2
|
|
gptkbp:B_10
|
5/66
|
|
gptkbp:B_12
|
-691/2730
|
|
gptkbp:B_14
|
7/6
|
|
gptkbp:B_16
|
-3617/510
|
|
gptkbp:B_18
|
43867/798
|
|
gptkbp:B_2
|
1/6
|
|
gptkbp:B_20
|
-174611/330
|
|
gptkbp:B_4
|
-1/30
|
|
gptkbp:B_6
|
1/42
|
|
gptkbp:B_8
|
-1/30
|
|
gptkbp:category
|
integer sequences
special numbers
|
|
gptkbp:discoveredBy
|
gptkb:Jacob_Bernoulli
|
|
gptkbp:discoveredIn
|
1713
|
|
gptkbp:evenIndexedNonzero
|
true
|
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gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:first_terms
|
1
-1/2
1/6
|
|
gptkbp:generatingFunction
|
x/(e^x - 1)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Bernoulli numbers
|
|
gptkbp:namedAfter
|
gptkb:Jacob_Bernoulli
|
|
gptkbp:notation
|
B_n
|
|
gptkbp:oddIndexedNonzero
|
false (except B_1)
|
|
gptkbp:OEIS
|
gptkb:A000367
|
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gptkbp:recurrence
|
B_0 = 1, sum_{k=0}^{n} (n+1 choose k) B_k = 0 for n > 0
|
|
gptkbp:relatedTo
|
gptkb:Euler_numbers
gptkb:Stirling_numbers
gptkb:Tangent_numbers
gptkb:Faulhaber's_formula
|
|
gptkbp:sequence
|
rational numbers
alternating sign
|
|
gptkbp:usedIn
|
gptkb:Riemann_zeta_function
gptkb:Euler–Maclaurin_formula
analysis
calculus
number theory
combinatorics
summation of powers
|
|
gptkbp:zeroOddIndex
|
true (except B_1)
|
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gptkbp:bfsParent
|
gptkb:Riemann_zeta_function
gptkb:Riemann_zeta_function_(when_χ_is_trivial)
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|
gptkbp:bfsLayer
|
5
|