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A procedure is proposed in order to expand where belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) (). We first derive a linear differential equation of order satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients . We develop in detail the two cases , and give the recurrencerelation in some cases (N=3,4), when the polynomials are monic Hermite orthogonal polynomials.
Let be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in , in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by .
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