Phrase guide

Maclaurin series

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.

Sound

Pronunciation

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1

noun

Meaning 1

Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x2+(f'(0))/(3!)x3+⋯=∑n=0 ᪲(f(n)(0))/(n!),xn.

Definition source: English Wiktionary via Wiktextract

Topics: calculus, mathematics, sciences

Examples

  • 1995, Ralph P. Boas, Gerald L. Alexanderson (editor), Dale H. Mugler (editor), Lion Hunting and Other Mathematical Pursuits, Mathematical Association of America, page 88, If the Maclaurin series of f and g converge for |z| < r and g(z) ≠ 0 for 0 ≤ |z| < r, then if the Maclaurin series for f is divided by the Maclaurin series for g by long division (as if the series were polynomials), the resulting series represents f / g for |z| < r.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.

Across languages

Translations

18 source translations are retained for this English entry.

  • Asturian: serie de Maclaurin — Taylor series centred at 0
  • Bulgarian: ред на Маклорен (red na Makloren) — Taylor series centred at 0
  • Catalan: sèrie de Maclaurin — Taylor series centred at 0
  • Chinese Mandarin: 麥克勞林級數 /麦克劳林级数 — Taylor series centred at 0
  • Chinese Mandarin: 馬克勞林級數 /马克劳林级数 — Taylor series centred at 0
  • Danish: Maclaurinrække — Taylor series centred at 0
  • Finnish: Maclaurinin sarja — Taylor series centred at 0
  • French: série de Maclaurin — Taylor series centred at 0
  • Galician: serie de Maclaurin — Taylor series centred at 0
  • German: Maclaurin-Reihe — Taylor series centred at 0
  • German: maclaurinsche Reihe — Taylor series centred at 0
  • Hungarian: Maclaurin-sor — Taylor series centred at 0
  • Italian: serie di Maclaurin — Taylor series centred at 0
  • Japanese: マクローリン級数 — Taylor series centred at 0
  • Polish: szereg Maclaurina — Taylor series centred at 0
  • Portuguese: série de Maclaurin — Taylor series centred at 0
  • Romanian: serie Maclaurin — Taylor series centred at 0
  • Spanish: serie de Maclaurin — Taylor series centred at 0