This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 InterpolatingFunction 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, Section 3.8.2. See also Implementation NotesA.9.44.25MainBookLinkOldButtonDataA.9.44.25. See also: CompiledFunction, FunctionInterpolation. Related package: NumericalMath`SplineFit`. Further Examples Here is a table of values of the reciprocal function and an InterpolatingFunction object that represents the data. In[1]:= Out[1]= In[2]:= Out[2]= An InterpolatingFunction object can be evaluated just like any other Mathematica function. The approximate function reproduces the values given at the data points and it gives approximate values in between. In[3]:= Out[3]= The approximate function is close to the original reciprocal function for most values in the domain. Evaluate the cell to see the graphic. In[4]:= In[5]:=