Christoffel-Darboux formula

Named after Elwin Bruno Christoffel and Jean Gaston Darboux.

the Christoffel-Darboux formula

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

• Christoffel-Darboux theorem