MathLiveMaclaurin series
Expresses a function as an infinite power series in x using its derivatives evaluated at zero. It is the Taylor series centred at the origin and is used to approximate functions near x = 0.
f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^nWhat the symbols mean
| the function being expanded | |
| index of the term, a non-negative integer | |
| the n-th derivative of f evaluated at x = 0 | |
| factorial of n | |
| independent variable |
About this formula
- FieldMathematics
- TopicSeries expansions
- LevelUniversity
- Also calledTaylor series at zero, Maclaurin expansion, power series expansion around 0, Taylor expansion at origin, series expansion of a function at 0
- SourceWikidata Q1882442
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