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Re: Generating a function from a series
*To*: mathgroup at smc.vnet.net
*Subject*: [mg65378] Re: [mg65354] Generating a function from a series
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Wed, 29 Mar 2006 06:34:17 -0500 (EST)
*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst
*References*: <200603280905.EAA26312@smc.vnet.net>
*Reply-to*: murray at math.umass.edu
*Sender*: owner-wri-mathgroup at wolfram.com
The section of The Mathematica Book where Series is introduced explains
the Normal function, to convert a SeriesData expression into a normal
expression by truncating higher-order terms.
f[x_] := Sin[x]
Series[f[x], {x, 0, 3}] // InputForm
SeriesData[x, 0, {1, 0, -1/6}, 1, 4, 1]
Normal[Series[f[x], {x, 0, 3}]] // InputForm
x - x^3/6
sf[x_] := Evaluate[Normal[Series[f[x], {x, 0, 3}]]]
Plot[sf[x], {x, -1, 1}]
(* works now as expected *)
Geico Caveman wrote:
> How does one generate a function from a series ?
>
> For example :
>
> sf=Series[f(x),{x,0,3}];
> fs[y_]=sf/.x->y
>
> Now this leaves that pesky O(()^4) term in the function definition,
> rendering the function useless for plots etc. How do I get rid of it ?
>
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
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