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In this paper, we solve the duplication problem P n (ax) = n m=0 C m (n, a)P m (x), where {P n } n≥0 belongs to a wide class of polynomials, including the classical orthogonal poly-nomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form… (More)

We consider the problem of finding explicit formulae, recurrence relations and sign properties for both connection and linearization coefficients for generalized Hermite polynomials. The most computations are carried out by the computer algebra system Maple using appropriate algorithms.

This article deals with the problem of finding closed analytical formulae for generalized linearization coefficients for Jacobi polynomials. By considering some special cases we obtain a reduction formula using for this purpose symbolic computation, in particular Zeilberger's and Petkovsek's algorithms.

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