Second-order recurrence relation for the linearization coefficients of the classical orthogonal polynomials

Let Pk be any sequence of the classical orthogonal polynomials. We give explicitly a second-order recurrence relation (in k) for the coefficients in PiPj = ∑k = ¦i−j¦i + jc(i, j, k) Pk. This result is obtained by a method which is alternative to the one proposed recently by A. Ronveaux et al. Applications of the result to some named systems of classical orthogonal polynomials are given.