Re: Corresponding function to given values...
- To: mathgroup at smc.vnet.net
- Subject: [mg35984] Re: Corresponding function to given values...
- From: Bill Rowe <listuser at earthlink.net>
- Date: Sun, 11 Aug 2002 05:13:42 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On 8/9/02 at 4:05 PM, Sven.Richter at unibw-muenchen.de (Sven Richter)
wrote:
>Is there a possibility that Mathematica gives me a function to given
>pairs of values? In other words: I have several pairs like {1, 2}, {2,
>4}, {3, 9}. And I what like to know the corresponding function (what
>is in this example obviously f[x]=x^2).
There are infinitely many possible functions that can generate the particular list in your example.
Specifically f[x]:={x, x^2 +(x-1)(x-2)(x-3)g[x]} for any g[x] will work. For Mathematica to determine a specific function it would be necessary to make assumptions about g[x]. Any assumptions made are certain to be wrong for some problem.
If you know the relationship between the numbers is expressed by a polynomial, then you could use InterpolatingPolynomial
In[1]:=InterpolatingPolynomial[Table[{n, n^2}, {n, 3}], x] // Simplify
Out[1]=x^2