Christoffel–Darboux formula
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In mathematics, the Christoffel–Darboux formula or Christoffel–Darboux theorem is an identity for a sequence of orthogonal polynomials, introduced by Elwin Bruno Christoffel (1858) and Jean Gaston Darboux (1878). It states that
where fj(x) is the jth term of a set of orthogonal polynomials of squared norm hj and leading coefficient kj.
There is also a "confluent form" of this identity by taking limit: