Christoffel–Darboux formula
- Christoffel–Darboux formula
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In mathematics, the 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 norm hj and leading coefficient kj.
See also
References
- Andrews, George E.; Askey, Richard; Roy, Ranjan (1999), Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, ISBN 978-0-521-62321-6; 978-0-521-78988-2, MR1688958
- Christoffel, E. B. (1858), "Über die Gaußische Quadratur und eine Verallgemeinerung derselben." (in German), Journal für Reine und Angewandte Mathematik 55: 61–82, doi:10.1515/crll.1858.55.61, ISSN 0075-4102, http://resolver.sub.uni-goettingen.de/purl?GDZPPN002150239
- Darboux, Gaston (1878), "Mémoire sur l'approximation des fonctions de très-grands nombres, et sur une classe étendue de développements en série" (in French), Journal de Mathématiques Pures et Appliquées 4: 5–56, 377–416, JFM 10.0279.01
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