Taylor series

Etymology
Named after English mathematician, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician.

Noun

 * 1)  A power series representation of given infinitely differentiable function $$\textstyle f$$ whose terms are calculated from the function's arbitrary order derivatives at given reference point $$\textstyle a$$; the series $$\textstyle f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f(a)}{2!} (x-a)^2+\frac{f'(a)}{3!}(x-a)^3+ \cdots = \sum_{n=0} ^ {\infty} \frac {f^{(n)}(a)}{n!} (x-a)^{n}$$.

Translations

 * Chinese:
 * Mandarin: 泰勒展開式
 * Czech: Taylorova řada
 * Danish: Taylorrække
 * German: Taylorreihe
 * Hungarian:
 * Italian:
 * Romanian: serie Taylor
 * Russian: ряд Те́йлора