Let {p_n(x)} be orthogonal polynomials associated with the distribution d α(x) on the interval [a, b]. Also let ρ congruent c(x - x_1)(x - x_2)...(x - x_l) (for c!=0) be a polynomial of order l which is nonnegative in this interval. Then the orthogonal polynomials {q(x)} associated with the distribution ρ(x) d α(x) can be represented in terms of the polynomials p_n(x) as ρ(x) q_n(x) = left bracketing bar p_n(x) | p_(n + 1)(x) | ... | p_(n + l)(x) p_n(x_1) | p_(n + 1)(x_1) | ... | p_(n + l)(x_1) ⋮ | ⋮ | ⋱ | ⋮ p_n(x_l) | p_(n + 1)(x_l) | ... | p_(n + l)(x_l) right bracketing bar .

Christoffel-Darboux identity | orthogonal polynomials