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BUILT-IN MATHEMATICA SYMBOL

FunctionInterpolation

evaluates expr with x running from

and constructs an InterpolatingFunction object which represents an approximate function corresponding to the result.

constructs an InterpolatingFunction object with several arguments.

You can use FunctionInterpolation to generate a single InterpolatingFunction object from an expression containing several such objects.

Computes an InterpolatingFunction representation of Exp[-Sin[x]^2]:

Use the resulting function as any function:

Computes an InterpolatingFunction representation of Exp[-Sin[x]^2]:

Out[1]=

Use the resulting function as any function:

Out[2]=

Use derivatives to improve the smoothness of the approximation: