Meanings
- calculusAny 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.
Analytically there are, of course, two Jacobi series branching off the Maclaurin series, but they are geometrically and physically identical, and involve only an interchange of a and b.
1953, Raymond Lyttleton, The Stability of Rotating Liquid Masses, Paperback edition, Cambridge University Press, published 2013, page 422 more 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.
It was almost as a by-product of this work that, in the first Turin memoir, he proved the convergence of the Maclaurin series of a function up to the singularity nearest to the origin (Section 7.5); it was in this context that he created what he called 'calculus of limits', later known as the method of majorants.
1997, Frank Smithies, Cauchy and the Creation of Complex Function Theory, Cambridge University Press, page 203
Origin
Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.
Full word history & related roots →Translations
Bulgarian ред на Маклорен
- ред на Маклорен (red na Makloren)Taylor series centred at 0
Catalan sèrie de Maclaurin
- sèrie de MaclaurinTaylor series centred at 0
Chinese Mandarin 麥克勞林級數 /麦克劳林级数, 馬克勞林級數 /马克劳林级数
- 麥克勞林級數 /麦克劳林级数Taylor series centred at 0
- 馬克勞林級數 /马克劳林级数Taylor series centred at 0
Danish Maclaurinrække
- MaclaurinrækkeTaylor series centred at 0
Finnish Maclaurinin sarja
- Maclaurinin sarjaTaylor series centred at 0
French série de Maclaurin
- série de MaclaurinTaylor series centred at 0
German Maclaurin-Reihe, maclaurinsche Reihe
- Maclaurin-ReiheTaylor series centred at 0
- maclaurinsche ReiheTaylor series centred at 0
Hungarian Maclaurin-sor
- Maclaurin-sorTaylor series centred at 0
Italian serie di Maclaurin
- serie di MaclaurinTaylor series centred at 0
Japanese マクローリン級数
- マクローリン級数Taylor series centred at 0
Polish szereg Maclaurina
- szereg MaclaurinaTaylor series centred at 0
Portuguese série de Maclaurin
- série de MaclaurinTaylor series centred at 0
Romanian serie Maclaurin
- serie MaclaurinTaylor series centred at 0
Spanish serie de Maclaurin
- serie de MaclaurinTaylor series centred at 0
Cite this entry
Maclaurin series. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Maclaurin%20series
“Maclaurin series.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Maclaurin%20series. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “Maclaurin series,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Maclaurin%20series.
Source: Maclaurin series on Wiktionary, CC BY-SA 4.0.