Let f (x0), f (x1), ..., f (xn) be n 1 entries of a function y = f (x), where f (x) is assumed too be polynomial corresponding to the arguments x0, x1, ...,xn.
The polynomial f (x) may be written as;
where A0,A1, ...,An are constants to be determined.
Putting x = x0
Putting x = x1
Hence, on substituting the constants values, we get
This result is known as Lagrange’s Interpolation Formula.