Difference between Taylor and MacLaurin Series-Usage

[Conservation]

Hi all,

I understand the numerical difference between a Taylor and Maclaurin Series; Maclaurin series is just Taylor Series about x=0. However, is there any difference between their usage?

I'm guessing Taylor series may be more accurate with less terms for approximating something close to its center; ex. finding f(2.1) for Taylor series about x=2 rather than using Maclaurin series. Am I correct in this assumption? What makes using one better than using the other?

Thanks.

 

[lurflurf]

Yes it may be better to use the series about 2 to find f(2.1) than the series about 0. We can do this with the Maclaurin Series though just find the series about 0 of f(x+2)

Since the Taylor series about a of f(x) is the same as the Maclaurin series of f(x+a) the two can be considered the same.

 

[HallsofIvy]

A word about terminology: you are really talking about Taylor and MacLaurin polynomials (truncated series) not the series themselves. There is no question of "accuracy" with Taylor and MacLaurin series.