Taylor series
Serie de Taylor
- Date
- 1715 · confidence high
- Place
- London, England
- Credited to
- Brook Taylor (Methodus incrementorum); special case by Maclaurin (1742); earlier work by Gregory and Newton
- People
- 👤 Brook Taylor1685–1731
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Every sufficiently smooth function can be expressed as a power series determined by its derivatives at a point. It turns calculus into a universal tool of approximation.
James Gregory knew the series in 1671; the formula's importance was only appreciated with Lagrange (1772), who gave the form of the remainder.
What it led to
- numerical analysis
- the theory of analytic functions
- perturbation physics
- Runge-Kutta methods
Built on
- Mercator seriesc. 1668
- Newton and Leibniz's calculus
- Madhava-Gregory series
Made possible
- Euler formula and Euler identity1748
- calculators and computers (function evaluation)