AbstractIn this paper, a general method is presented that allows the derivation of the expansion coefficients of the product of two orthogonal functions provided the generating function is known. For the three classical orthogonal polynomials, the Laguerre, the Hermite, and the Legendre polynomials, the coefficients blmn with ϕmϕn = ∑lblmnϕl are derived. © 1993 John Wiley & Sons, Inc.