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词汇 Taylor's series
释义

Definition of Taylor's series in English:

Taylor's series

noun
Mathematics

  • 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.

    〔数〕泰勒级数

    Example sentencesExamples
    • This work was highly praised by Lagrange, who gave a similar theory enriched by the Lagrange Remainder for the Taylor series.
    • One feature was his refutation in 1822 by counterexamples of Lagrange's belief that a function can always be expanded in a Taylor series.
    • Their explanation of why a Taylor series represents a function is incorrect, and they don't discuss the justification for term-by-term differentiation.
    • The same principle could be applied to a polynomial of any degree or to a Taylor series of an analytic function.
    • 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.

Origin

Early 19th century: named after Brook Taylor (1685–1731), English mathematician.
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