Definition of Taylor's series in English:

Taylor's series

Line breaks: Taylor's ser¦ies


  • 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.
    More example sentences
    • 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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