The Full Wiki

More info on Christoffel–Darboux formula

Christoffel–Darboux formula: Wikis


Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.


From Wikipedia, the free encyclopedia

In mathematics, the ChristoffelDarboux theorem converts a linear operator on a linear subspace into a symmetric kernel. From the projection operator,

 J_n(x,y) = \sum_{j=0}^n \frac{f_j(x) f_j(y)}{h_j}

where fj(x) is the j^{\,th} term of a set of orthogonal polynomials, results the Christoffel–Darboux Theorem[1]:

 J_n (x,y) = \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}.
  1. ^


Got something to say? Make a comment.
Your name
Your email address