Let the values of a function *y* = *f*(*x*) be given at different *x* values; thus,

Then *interpolation* means to find an approximate value of *f*(*x*) for an *x* between two *x*-values in (*x*_{0}, *x*_{n}). This is done by finding a polynomial called an *interpolating polynomial* which agrees with the function at the nodal points *x*_{i} (*i* = 0, 1, 2, …, *n*). In finding a suitable interpolating polynomial we need to have a formula for errors in polynomial approximation.

Let *y* = *f*(*x*) be a function defined at the (*n* + 1) points

(*x*_{i}, *y*_{i}) (*i* = 0, 1, 2, …, *n*) (4.1)

Suppose *f*(*x*) is ...

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