Maclaurin series en · NOUN
Etymology
Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.
Meanings
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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.
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: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 42:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Maclaurin series | Number=Plur | lexicographic |
Hypernyms
power series (Taylor series centred at 0) · Taylor series (Taylor series centred at 0)
Translations (18)
hu Maclaurin-sor (Taylor series centred at 0) · cmn 馬克勞林級數 /马克劳林级数 (Taylor series centred at 0) · de maclaurinsche Reihe (Taylor series centred at 0) · pt série de Maclaurin (Taylor series centred at 0) · fr série de Maclaurin (Taylor series centred at 0) · es serie de Maclaurin (Taylor series centred at 0) · ja マクローリン級数 (Taylor series centred at 0) · gl serie de Maclaurin (Taylor series centred at 0) · ro serie Maclaurin (Taylor series centred at 0) · pl szereg Maclaurina (Taylor series centred at 0) · ast serie de Maclaurin (Taylor series centred at 0) · cmn 麥克勞林級數 /麦克劳林级数 (Taylor series centred at 0) · it serie di Maclaurin (Taylor series centred at 0) · da Maclaurinrække (Taylor series centred at 0) · de Maclaurin-Reihe (Taylor series centred at 0) · ca sèrie de Maclaurin (Taylor series centred at 0) · fi Maclaurinin sarja (Taylor series centred at 0) · bg ред на Маклорен (Taylor series centred at 0)