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Questions on the interpolation functions in Mathematica (InterpolatingFunction[], Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)

Wolfram Documentation: InterpolatingFunction, Interpolation, ListInterpolation, FunctionInterpolation, InterpolatingPolynomial

Constructing InterpolatingFunctions:

Manipulating InterpolatingFunctions:

InterpolatingFunction Internals: