Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case

We present a simple approach in order to compute recursively the connection coefficients between two families of classical (continuous) orthogonal polynomials (Hermite, Laguerre, Jacobi and Bessel), i.e. the coefficients Cm(n) in the expression Pn(x) = ∑m=0n (m (n)Qm(x), where {Pn(x)} and {Qm(x)} belong to the aforementioned class of polynomials. This is done by adapting a general and systematic algorithm, recently developed by the authors, to the classical situation. Moreover, extensions of this method to some related connection problems and to the generalized linearization problem are given.