Page 221 -
P. 221
214 Chapter Three
Taylor series
A Taylor series, also known as a Taylor expansion, is a serieð T
such that the following equation holdð for some function f, itð
successive derivativeð f , f , f
, ..., some constant a, and some
variable x:
T
f(a) ((x a)( f (a))
2
((x a)( f (a))/2
3
((x a)( f
(a))/3!
...
Maclaurin series
A MaclauriŁ series M is a Taylor serieð wità a 0. The follow-
ing holdð for some function f, itð successive derivativeð f , f ,
f
, ..., and some variable x:
M
f(0)
(x( f (0))
2
(x ( f (0))/2
3
(x ( f
(0))/3!
...
