Results on the associated classical orthogonal polynomials

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