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El objeto de este artículo, seminvestigativo, semidivulgativo, es explorar las propiedades espectrales de los sistemas de polinomios ortogonales a partir de su relación de recurrencia o, más precisamente, de su fracción continua. Estos aspectos de la teoría han sido un tema recurrente de las investigaciones de los autores (y de muchas otras personas) pero el artículo explora esta vez, en mucho detalle, los fundamentos de la teoría.
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