       Re: inverse command of Series[]

• To: mathgroup at smc.vnet.net
• Subject: [mg8054] Re: inverse command of Series[]
• From: weber at math.uni-bonn.de (Matthias Weber)
• Date: Mon, 4 Aug 1997 01:47:37 -0400
• Organization: RHRZ - University of Bonn (Germany)
• Sender: owner-wri-mathgroup at wolfram.com

```In article <5s0v3n\$q7n\$1 at dragonfly.wolfram.com>, "Nguyen N. Anh"
<anh at chm.ulaval.ca> wrote:

> Hello,
>
> I've written a program in Mathematica and it works quite well. However, after
> convergence it gave as  result the following polinomial:
>
> 1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120 + x^6/720 + x^7/5040
>
> I know that this is the power series expansion of function E^x but I want that
> my program recognizes it automatically and  outputs the generating function of
> the polinomial calculated ( E^x in this case).
>
> Is there any command or package which can do that ?
>
> Any help will be appreciated
>
> Regards
>

Here is a suggestion how to 'recognize' a polynomial as a
truncated power series:

Let us assume that the function you want to recognize
satisfies some linear ode of order n. You can get its coefficients approximately
by differentiating the polynomial n times and finding the coefficients
of a linear combination which makes this zero.
Then you can solve this ode explicitly, giving you the required function.

For other types of functions, you might be able to modify this
approach.

However, you should be aware that this procedure will not
prove anything.

Good luck,

Matthias Weber

```

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