Christoffel-Darboux formula

proper noun

An identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ.

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Meanings

proper nounthe Christoffel-Darboux formula
  1. mathematicsAn identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ.

Origin

Named after Elwin Bruno Christoffel and Jean Gaston Darboux.

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Cite this entry
APA

Christoffel-Darboux formula. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Christoffel-Darboux%20formula

MLA

“Christoffel-Darboux formula.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Christoffel-Darboux%20formula. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Christoffel-Darboux formula,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Christoffel-Darboux%20formula.

Source: Christoffel-Darboux formula on Wiktionary, CC BY-SA 4.0.