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BernoulliB ​

The nth Bernoulli number, a rational sequence appearing in power-sum (Faulhaber) formulas and series expansions.

WikipediaBernoulli numberMathWorldBernoulliNumberWikidataQ694114nLabBernoulli numberDLMF24.2.iFungrimBernoulliB✓Fungrim entryOEISA027641A027642Wolfram LanguageBernoulliB✓
BernoulliB(n)the nth Bernoulli number .
SageMathbernoulli(n)SymPybernoulli(n)

Domain: Sequences

Details
  • Defined by the generating function .
  • for every odd ; under this (the "") convention.
  • Drive Faulhaber's formula for power sums, . See Binomial.
  • Related to the Riemann zeta function: for , and .
  • compute-engine only defines for nonnegative integer ; the two-argument Bernoulli polynomial is not yet supported.

Examples