Taylor series

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Taylor series

[′tā·lər ‚sir·ēz]
(mathematics)
The Taylor series corresponding to a function ƒ(x) at a point x0 is the infinite series whose n th term is (1/ n !)·ƒ(n)(x0)(x-x0) n , where ƒ(n)(x) denotes the n th derivative of ƒ(x).
(naval architecture)
Resistance charts based upon model tests of a series of ships derived by altering the proportions of a single parent form; used to study the effects of these alterations on resistance to the ship's motion, and to predict the powering requirements for new ships.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In 1985, Louis de Branges de Bourcia proved the Bieberbach conjecture, i.e., for a univalent function its [n.sup.th] Taylor coefficient is bounded by n (see [3]).
By using the Taylor expansion (5) for f [member of] [SIGMA](p) and the Taylor coefficient estimate (6) for |[a.su.n]|, we have for 0 < r < p,
Note, however, that even for moderate steady-state inflation, it takes a large coefficient on output to generate determinacy in a rule that includes the standard Taylor coefficient, [f.sub.y] = 0.125, on output.
On the other hand, it is well known (see e.g., [3]) that the value [sigma]([z.sub.i]) of the parameter a in (2.8) at the interpolation node [z.sub.i] completely determines the ([n.sub.i] + 1)-th Taylor coefficient [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
As a result, we get a linear system for which the solution of this system yields the unknown Taylor coefficients of the solution functions.
Clearly, the third equality in (22) is concerned with Markov parameters, which are defined as Taylor coefficients of the transfer function in the frequency domain when it is expanded around the infinity [4].
This is so because the coefficients [c.sub.n] are the Taylor coefficients at u = 0 of the function h(u) = g(t)[dt/du], which is defined in an implicit form because, in general, the function t(u) is not explicitly known.
If f [member of] [S.sup.0.sub.H] for which f(D) is convex, Clunie and Sheil- Small [14] proved that the Taylor coefficients of h and g satisfy the inequalities
Then, the Taylor coefficients of f(z) are given by the following finite sum
Following this procedure, which can be easily programmed using symbolic algebra [33], the Taylor coefficients up to a desired order n can be obtained.
Here [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] [member of] C and the [a.sub.j] are the Taylor coefficients of f.
For identical diodes, [g.sub.1] = [g'.sub.1], [g.sub.2] = -[g'.sub.2], [g.sub.3] = [g'.sub.3], [c.sub.1] = [c'.sub.1], [c.sub.2] = -[c'.sub.2] and [c.sub.3] = [c'.sub.3], hence, [Y.sub.1] = [Y'.sub.1] [g.sub.i] and [c.sub.i] for i = 1 to 3 are the first three Taylor coefficients of the conductances and capacitors of the diode, respectively.