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MathGroup Archive 2006

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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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