Christoffel–Darboux formula
Encyclopedia
In mathematics, the Christoffel–Darboux theorem is an identity for a sequence of orthogonal polynomials
, introduced by and . It states that
where
is the jth term of a set of orthogonal polynomials
of norm hj and leading coefficient kj.
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
, introduced by and . It states that
where
is the jth term of a set of orthogonal polynomialsOrthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
of norm hj and leading coefficient kj.