Taylor series
noun Etymology: Brook Taylor died 1731 English mathematician Date: 1842 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 f(x) = f(a) + (f[1](a)/1!)(x - a) + (f[2](a)/2!)(x - a)² + ... + (f[n](a)/n!)(x - a)ⁿ + ... where f [n](a) is the derivative of nth order of f(x) evaluated at a — called also Taylor's series

New Collegiate Dictionary. 2001.

Look at other dictionaries:

  • Taylor series — Series expansion redirects here. For other notions of the term, see series (mathematics). As the degree of the Taylor polynomia …   Wikipedia

  • Taylor series — Teiloro eilutė statusas T sritis fizika atitikmenys: angl. Taylor series vok. Taylorsche Reihe, f rus. ряд Тэйлора, m pranc. série de Taylor, f; série taylorienne, f …   Fizikos terminų žodynas

  • Taylor series — Math. an approximation of a given function f at a particular point x, in terms of values of the function and its derivatives at a neighboring point x0, by a power series in which the terms are given by f(n)(x0) (x x0)n/n!, where f(n)(x0) is the… …   Universalium

  • taylor series — ˈtālə(r) noun also taylor s series ə(r)(z) Usage: usually capitalized T Etymology: after Brook Taylor died 1731 English mathematician : a power series that gives the expansion of a function f( …   Useful english dictionary

  • Probabilistic interpretation of Taylor series — In mathematics, the Taylor series is a power series associated to a function. From a probabilistic point of view, the Taylor series is the most natural approximation of that function.More precisely, the Taylor polynomial of degree , n , is the… …   Wikipedia

  • Taylor — is an English surname and given name meaning tailor . It may also refer to: *Taylor (given name), the given name * See also List of people with surname TaylorPlaces* Australia ** Electoral district of Taylor, state electoral district ** Taylor,… …   Wikipedia

  • Taylor's theorem — In calculus, Taylor s theorem gives a sequence of approximations of a differentiable function around a given point by polynomials (the Taylor polynomials of that function) whose coefficients depend only on the derivatives of the function at that… …   Wikipedia

  • Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

  • Taylor-Entwicklung — In der Analysis verwendet man Taylorreihen (auch Taylor Entwicklungen oder Taylor Näherung), um Funktionen in der Umgebung bestimmter Punkte durch Potenzreihen darzustellen. So kann ein komplizierter analytischer Ausdruck durch eine nach wenigen… …   Deutsch Wikipedia

  • Taylor-Näherung — In der Analysis verwendet man Taylorreihen (auch Taylor Entwicklungen oder Taylor Näherung), um Funktionen in der Umgebung bestimmter Punkte durch Potenzreihen darzustellen. So kann ein komplizierter analytischer Ausdruck durch eine nach wenigen… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”