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Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials

Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials

Let $\{ P_k\} $ be any sequence of classical orthogonal polynomials. Further, let $f$ be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfi