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

Stanislaw Lewanowicz (2002)

Applicationes Mathematicae

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 satisfied by the coefficients a k in f = k a k P k . A systematic use of the basic properties (including some nonstandard ones) of the polynomials P k results in obtaining a low order of the recurrence.

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