Re: how to have the functional form from an interpolation

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• Subject: [mg130270] Re: how to have the functional form from an interpolation
• From: debguy <johnandsara2 at cox.net>
• Date: Sun, 31 Mar 2013 03:11:30 -0400 (EDT)
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```"Now I would like to have the explicit form of the function. Is there
a way in which I can get it?"

Question is do you want it?  The topic of curve fitting functions is
very complex.  Why not use the result and move on?

The Mathematica Book has no lack of explaining Interpolation topics in
many sections. (wikipedia.com goes into more depth)

(from the book) "InterpolatingFunction uses divided differences to
construct Lagrange or Hermite interpolating polynomials".  This means
if you take the parameters from the result and apply them in the
mentioned polynomials you have the equation for that particular
Mathematica function.

But what explicit form is a result, and the quality of the results,
depends on what interpolation function you use.

If you want to fit curves and see the equations I suggest using a
simpler curve fitter like Polynomial Fit: which has simpler results.
For a more general way use Fourier to get a series of sin cos terms
you can see: can be lengthy, but works.

As far as a general way to fit any data and see the function: no.
Mathematica isn't built to show the symbolic equation for everything
it does.  Some are proprietary.  Some are internal for speed reasons.
And they do tell you what the results stand for (see above).  Not all
data can be fitted, and that starts a whether to use Statistics
question.

```

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