Maclaurin series

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

Noun

 * 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 $$\textstyle f$$, the power series $$\textstyle f(0)+\frac {f'(0)}{1!}x+ \frac{f(0)}{2!}x^2+ \frac{f'(0)}{3!}x^3+ \cdots = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} \, x^{n}$$.
 * 2) * 1995, Ralph P. Boas, Gerald L. Alexanderson (editor), Dale H. Mugler (editor), Lion Hunting and Other Mathematical Pursuits,, 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.
 * 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.

Translations

 * Chinese:
 * Mandarin: 馬克勞林級數
 * Danish: Maclaurinrække
 * German: Maclaurin-Reihe, maclaurinsche Reihe
 * Italian: serie di Maclaurin
 * Japanese: マクローリン級数
 * Romanian: serie Maclaurin