Maclaurin series
English
Etymology
Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.
Noun
Maclaurin series (plural Maclaurin series)
- (calculus) 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 , the power series .
- 1953, Raymond Lyttleton, The Stability of Rotating Liquid Masses, Cambridge University Press, 2013, Paperback Edition, page 42,
- 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.
- 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.
- 1997, Frank Smithies, Cauchy and the Creation of Complex Function Theory, Cambridge University Press, page 203,
- 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.
- 1953, Raymond Lyttleton, The Stability of Rotating Liquid Masses, Cambridge University Press, 2013, Paperback Edition, page 42,
Hypernyms
- (Taylor series centred at 0): power series, Taylor series
Translations
Taylor series centred at 0
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