Phrase guide

Bernoulli number

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

Any one of the rational numbers in a sequence of such that appears in numerous contexts, including formulae for sums of integer powers and certain power series expansions.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, number-theory, sciences

Examples

  • 1993, Serge Lang, Complex Analysis, Springer, 3rd Edition, page 418, The assertion about the value of the zeta function at negative integers then comes immediately from the definition of the Bernoulli numbers in terms of the coefficients of a power series, namely t/(et-1)=∑n=0 ᪲B_n(tn)/(n!)

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after Swiss mathematician Jacob Bernoulli (1654–1705), who discovered the numbers independently of and at about the same time as Japanese mathematician Seki Kōwa. The numbers first appeared as coefficients in Bernoulli's formulae for the sum of the first n positive integers, each raised to a given power. The sequence was subsequently found in numerous other contexts.