Definition of Taylor series in US English:

Taylor series


  • An infinite sum giving the value of a function f(z) in the neighborhood 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.’
    • ‘Their explanation of why a Taylor series represents a function is incorrect, and they don't discuss the justification for term-by-term differentiation.’
    • ‘An approximate method for calculating the bias and variance of a statistic is to expand it as a Taylor series about the true value and examine the expectations of the lower-order terms.’
    • ‘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.