       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

```

• Prev by Date: Re: question about the inverse li function
• Next by Date: RootSearch options
• Previous by thread: Re: Generating a function from a series
• Next by thread: Re: Generating a function from a series