This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

InterpolatingPolynomial

 InterpolatingPolynomial[{f1, f2, ...}, x]constructs an interpolating polynomial in x which reproduces the function values at successive integer values of . InterpolatingPolynomial[{{x1, f1}, {x2, f2}, ...}, x]constructs an interpolating polynomial for the function values corresponding to values . InterpolatingPolynomial[{{{x1, y1, ...}, f1}, {{x2, y2, ...}, f2}, ...}, {x, y, ...}]constructs a multidimensional interpolating polynomial in the variables . InterpolatingPolynomial[{{{x1, ...}, f1, df1, ...}, ...}, {x, ...}]constructs an interpolating polynomial that reproduces derivatives as well as function values.
• The function values and sample points , etc. can be arbitrary real or complex numbers, and in 1D can be arbitrary symbolic expressions.
• With any given specified set of data, there are infinitely many possible interpolating polynomials; InterpolatingPolynomial always tries to find the one with lowest total degree.
• Different elements in the data can have different numbers of derivatives specified.
• For multidimensional data, the derivative can be given as a tensor with a structure corresponding to D[f, {{x, y, ...}, n}].  »
• InterpolatingPolynomial allows any function value or derivative to be given as Automatic, in which case it will attempt to fill in the necessary information from derivatives or other function values.  »
• The option setting Modulus->n specifies that the interpolating polynomial should be found modulo .  »
Construct an interpolating polynomial for the squares:
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Check the result:
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Construct an interpolating polynomial through three points:
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Check the result at a single point:
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 Scope   (3)
 Options   (1)
 Applications   (5)