Christoffel Formula

Let  be orthogonal polynomials associated with the distribution  on the interval . Also let

(for ) be a polynomial of order  which is nonnegative in this interval. Then the orthogonal polynomials associated with the distribution  can be represented in terms of the polynomials  as

In the case of a zero  of multiplicity , we replace the corresponding rows by the derivatives of order 0, 1, 2, ...,  of the polynomials , ...,  at .

REFERENCES:

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., pp. 29-30, 1975.