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Bernoulli number
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rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯
In the Vinony graph
Within Vinony's link graph, Bernoulli number is referenced by 267 other articles, and connects out to Alternating permutation, trigonometric function and calculus.
It is catalogued under topics including Integer sequences, Number theory and Topology.
Its subject is documented across 39 Wikipedia language editions.
Wikidata facts
- Image
- Bernoulli numbers logarithmic growth.png
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- Stack Exchange tag
- stackoverflow.com/tags/bernoulli-numbers
- time of discovery or invention
- 1710-00-00
- Commons category
- Bernoulli numbers
via Wikidata · CC0
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Encyclopedic overview
In mathematics, the Bernoulli numbers Bn are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function.
The values of the first 20 Bernoulli numbers are given in the adjacent table. Two conventions are used in the literature, denoted here by
Excerpted from Wikipedia’s “Bernoulli number” article, available under the CC BY-SA 4.0 licence.