MathLiveTaylor series
Expresses an infinitely differentiable function as an infinite sum of terms built from its derivatives at a single point a. The sum equals the function only where the series converges to it (for example, for analytic functions near a), and truncated sums are used to approximate functions by polynomials and to analyse their behaviour near that point.
f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x - a)^nWhat the symbols mean
| the function being expanded | |
| the point around which the expansion is centred | |
| index of the summation, a non-negative integer | |
| the n-th derivative of f evaluated at a | |
| the factorial of n | |
| the variable at which the function is evaluated |
About this formula
- FieldMathematics
- TopicCalculus and series
- LevelUniversity
- Also calledTaylor expansion, power series expansion of a function, expansion of a function as infinite sum, Taylor series formula, Taylor expansion around a point
- SourceWikidata Q131187
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