Secondary polynomials

In mathematics, the secondary polynomials formula_1 associated with a sequence formula_2 of polynomials orthogonal with respect to a density formula_3 are defined by
To see that the functions formula_5 are indeed polynomials, consider the simple example of formula_6 Then,
which is a polynomial formula_8 provided that the three integrals in formula_9 (the moments of the density formula_10) are convergent.