Maclaurin's theorem (English)
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Definition (advanced level)
The special case of Taylor's theorem when a=0, i.e.
for a given function f whose (n−1)th derivative is continuous in [0,b] and whose nth derivative exists in (0,b), we can write f(x) as a Taylor series ie:
(x must lie in [0,b].) Rn is a remainder term; it can be written in various forms; its value is usually small.
for a given function f whose (n−1)th derivative is continuous in [0,b] and whose nth derivative exists in (0,b), we can write f(x) as a Taylor series ie:
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Relations
- broader:
- (en) Taylor's theorem
- references:
- (en) Maclaurin series
- referenced:
- (en) Error term
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