Christoffel-Darboux formula

English

Named after Elwin Bruno Christoffel and Jean Gaston Darboux.

Template:Lb An identity for a sequence of orthogonal polynomials: $\sum_{j = 0}^{n} \frac{f_{j} (x) f_{j} (y)}{h_{j}} = \frac{k_{n}}{h_{n} k_{n + 1}} \frac{f_{n} (y) f_{n + 1} (x) - f_{n + 1} (y) f_{n} (x)}{x - y}$ where f_j(x) is the jth term of a set of orthogonal polynomials of squared norm h_j and leading coefficient k_j.