Lagrange's interpolation formula

English Lagrange polynomial Etymology Named after Joseph Louis Lagrange (1736–1813), an Italian Enlightenment Era mathematician and astronomer. Noun - en mathematics A formula which when given a set of n points , gives back the unique polynomial of degree (at most) n − 1 in one variable which describes a function passing through those points. The formula is a sum of products, like so: . When then all terms in the sum other than the i th contain a factor in the numerator, which becomes equal to zero, thus all terms in the sum other than the i th vanish, and the i th term has factors both in the numerator and denominator, which simplify to yield 1, thus the polynomial should return as the function of for any i in the set . en eponyms