Maclaurin series

English

Etymology

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

Noun

1. Template:Lb 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 $f(0)+\frac{f^{\prime }(0)}{1!}x+\frac{f^{″}(0)}{2!}{x}^2+\frac{f^{‴}(0)}{3!}{x}^3+\cdots ={\sum }_{n=0}^{\mathrm{\infty }}\frac{f^{(n)}(0)}{n!}{x}^n$.
   • Template:Quote-book
   • 1995, Ralph P. Boas, Gerald L. Alexanderson (editor), Dale H. Mugler (editor), Lion Hunting and Other Mathematical Pursuits, Template:W, 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.

   • Template:Quote-book

Hypernyms

• Template:Sense Template:L, Template:L

Translations

• Chinese:

  Mandarin: Template:T

• Danish: Template:T
• Finnish: Template:T
• German: Template:T, Template:T
• Italian: Template:T
• Japanese: Template:T
• Polish: Template:T
• Romanian: Template:T