Taylor's series


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Related to Taylor's series: Maclaurin series

Taylor's series

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(Mathematics) maths 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. Under certain conditions, the series has the form f(z) = f(a) + [f′(a)(za)]/1! + [f″(a)(za)2]/2! + …. See also Maclaurin's series
[C18: named after Brook Taylor (1685–1731), English mathematician]
References in periodicals archive ?
Now, the Taylor's series expansions of [[summation].sup.p.sub.n=1][w.sub.i]f'([x.sub.n] + [[tau].sub.i]([z.sub.n]- [x.sub.n])) and [[summation].sup.p.sub.i=1][w.sub.i]f"([x.sub.n] + [[tau].sub.i]([z.sub.n] - [x.sub.n])) are given by
Our objective is to determine the coefficients [[u.bar].sub.js.sup.(n)](z, [alpha]) and [[bar.u].sub.js.sup.(n)](z, [alpha]), for n = 0,...,s and j = 1,...,m in system (7); thus we expand [[u.bar].sub.js](z, [alpha]) and [[u.bar].sub.js](z, [alpha]) in Taylor's series at arbitrary point z: a [less than or equal to] z [less than or equal to] b
The title is the first in Taylor's series Chronicles of St Mary's, which follows an eccentric group of historical researchers as they 'investigate' major historical events in contemporary time.
This approach is based on the use of Taylor's series expansion.
Further development of the classic Hertz-contact solution using higher-order terms of a Taylor's series expansion shows a quadratic rather than a linear relationship between the reduced elastic modulus and the resonant frequency shift.
Expressing the top wall velocity using Taylor's series expansion we get,
With the help of the calculator find the Taylor's series of the function G(x,r) and verify that the coefficients of [r.sup.n] are just the Legendre's polynomials [P.sub.n](x).
Expanding f ([z.sub.n]) by Taylor's series about w, we have:
It is known that the Taylor's series expansion as given in [1] for a function y(x) about the point x = a , where y(x) is continuous and possesses continuous derivatives of order (n+1) in an interval that contains the point x = a, is
In order to determine the conditional probability of liquefaction, the Taylor's Series reliability method and Monte Carlo simulation method are used.