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Interpolation[{f1, f2, ...}]
constructs an interpolation of the function values fi, assumed to correspond to x values 1, 2, ... .
Interpolation[{{x1, f1}, {x2, f2}, ...}]
constructs an interpolation of the function values fi corresponding to x values xi.
Interpolation[{{{x1, y1, ...}, f1}, {{x2, y2, ...}, f2}, ...}]
constructs an interpolation of multidimensional data.
Interpolation[{{{x1, ...}, f1, df1, ...}, ...}]
constructs an interpolation that reproduces derivatives as well as function values.
  • The interpolating function returned by Interpolation[data] is set up so as to agree with data at every point explicitly specified in data.
  • The function values fi can be real or complex numbers, or arbitrary symbolic expressions.
  • The fi can be lists or arrays of any dimension.
  • The function arguments xi, yi, etc. must be real numbers.
  • Different elements in the data can have different numbers of derivatives specified.
  • For multidimensional data, the n^(th) derivative can be given as a tensor with a structure corresponding to D[f, {{x, y, ...}, n}].
  • Interpolation works by fitting polynomial curves between successive data points.
  • Interpolation allows any derivative to be given as Automatic, in which case it will attempt to fill in the necessary information from other derivatives or function values.
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