Results on the associated classical orthogonal polynomials

Let {P-k(x)} be any system of the classical orthogonal polynomials, and let {P-k(x;c)} be the corresponding associated polynomials of order c (c is an element of N). Second-order recurrence-relation (in k) is given for the connection coefficient a(no1,k)((c)) in P-n-1(x;c) = (k=0)Sigma(n-1) a(n-1,k)((c))P-k((x)). This result is obtained thanks to a new explicit form of the fourth-order differential equation satisfied by P-n-1((.);c).