GENERALIZED LINEARIZATION PROBLEMS

We prove that if P-i(x) and ($) over bar P-j(x) are two families of se mi-classical orthogonal polynomials, all the linearization coefficient s L(i,j,k) occuring in the product of these two families satisfy a lin ear recurrence relation involving only the k index. This property also extends to the linearization coefficients arising from an arbitrary n umber of products of semi-classical orthogonal polynomials.