InterpolatingFunction[domain, table] represents an approximate function whose values are found by interpolation.
InterpolatingFunction works like Function.
InterpolatingFunction[ ... ][x] finds the value of an approximate function with a particular argument x.
In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by <>.
domain specifies the domain of the data from which the InterpolatingFunction was constructed.
If you supply arguments outside of the domain, a warning is generated, and then an extrapolated value is returned.
InterpolatingFunction objects that take any number of real arguments may be constructed.
You can take derivatives of InterpolatingFunction objects using D and Derivative.
NDSolve returns its results in terms of InterpolatingFunction objects.
See The Mathematica Book: Section 1.6.4, Section 2.2.8 and Section 3.8.2.
Implementation Notes: see section A.9.4.
See also: Interpolation, CompiledFunction, FunctionInterpolation.
Related package: NumericalMath`SplineFit`.