Christoffel-Darboux formula

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English

English Wikipedia has an article on:

Christoffel-Darboux formula

Etymology

Named after Elwin Bruno Christoffel and Jean Gaston Darboux.

Proper noun

the Christoffel-Darboux formula

(mathematics) 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.

Related terms

Christoffel-Darboux theorem

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