Taylor series

noun

Tay·lor series ˈtā-lər- How to pronounce Taylor series (audio)

: a power series that gives the expansion of a function f (x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function in which case it has the form {latex}f(x) = f(a) + \\frac{f'(a)}{1!}(x - a) + \\frac{f''(a)}{2!}(x - a)^{2} + \\dots + \\frac{f^{[n]}(a)}{n!}(x - a)^{n}{/latex} where f[ⁿ] (a) is the derivative of nth order of f(x) evaluated at a

called also Taylor's series

Word History

Etymology

Brook Taylor †1731 English mathematician

First Known Use

1842, in the meaning defined above

单词	Taylor series
释义	Taylor series noun Tay·lor series ˈtā-lər- : a power series that gives the expansion of a function f (x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function in which case it has the form {latex}f(x) = f(a) + \\frac{f'(a)}{1!}(x - a) + \\frac{f''(a)}{2!}(x - a)^{2} + \\dots + \\frac{f^{[n]}(a)}{n!}(x - a)^{n}{/latex} where f[ⁿ] (a) is the derivative of nth order of f(x) evaluated at a called also Taylor's series Word History Etymology Brook Taylor †1731 English mathematician First Known Use 1842, in the meaning defined above
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