Supriya Ghosh (Editor)

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

∑ j = 0 n f j ( x ) f j ( y ) h j = k n h n k 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.

References

Christoffel–Darboux formula Wikipedia
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