# Taylor series

(redirected from Taylor formula)

## 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 Section 3, we use the time scales Taylor formula, see [11, Theorem 1.113], i.e.,
and, by the time scales Taylor formula, more precisely, (2.1),
Taylor presented a semiempirical formula (Taylor formula) for the long cylindrical shell, and the projection angle of fragments can be obtained by using the Taylor formula [2].
In particular, we have also the following Taylor formula of order m for a function f in B[C.sup.m] (see [10,25]),
In [12] the following estimate of the remainder [R.sub.m](f; s, t) := [h.sub.s](t) [log.sup.m] t in the Taylor formula of order m is proved, which extends a result proved in [21] for the classical Taylor formula in a slightly different setting.
Moreover, in the past years, central bank has used McCallum and the Taylor formula based on quarter data as assistance by decision taking.
Analogously to [[summation].sub.2,1], here we can again use the Taylor formula to obtain
Using the modified Taylor formula we Get [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Formula (9.17) is the second Taylor formula of Theorem 9.2.
Hence, it is likely that after 2000 the Taylor formula does not accurately reflect the information used by the FOMC as input to its deliberations.
Note that the target funds rate predicted by the Taylor formula generally tracks the actual funds rate through 2000, though there are sizable and persistent deviations of the funds rate from the values predicted by the formula.
By Taylor formula in the local basis ([sigma][beta]) we get [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] and a similar formula for [P.sup.t.sub.[alpha]][[sigma].sup.2].

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