InterpolatingPolynomial[data, var] gives a polynomial in the variable var which provides an exact fit to a list of data.
The data can have the forms , , , , ... or , , ... , where in the second case, the are taken to have values 1, 2, ... .
The can be replaced by , , , ... , specifying derivatives at the points .
With a list of data of length , InterpolatingPolynomial gives a polynomial of degree .
Example: InterpolatingPolynomial[4, 5, 8, x] .
InterpolatingPolynomial gives the interpolating polynomial in Newton form, suitable for numerical evaluation.
See The Mathematica Book: Section 3.3.4 and Section 3.8.1.
See also: Fit, Roots.
Related package: NumericalMath`PolynomialFit`.