An infinite sum giving the value of a function f(z) in the neighbourhood of a point a in terms of the derivatives of the function evaluated at a.
- This work was highly praised by Lagrange, who gave a similar theory enriched by the Lagrange Remainder for the Taylor series.
- The same principle could be applied to a polynomial of any degree or to a Taylor series of an analytic function.
- One feature was his refutation in 1822 by counterexamples of Lagrange's belief that a function can always be expanded in a Taylor series.
Early 19th century: named after Brook Taylor (1685–1731), English mathematician.
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