A unified algorithmic framework interprets coefficient recurrences for orthogonal polynomial series as numerators of operator fractions and computes them via noncommutative Euclidean algorithm.
Rebillard.Étude théorique et algorithmique des séries de Chebyshev, solutions d’équations différentielles holonomes
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Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials
A unified algorithmic framework interprets coefficient recurrences for orthogonal polynomial series as numerators of operator fractions and computes them via noncommutative Euclidean algorithm.