2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152923The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence relations that correspond to multipoint rational interpolants. A Favard type theorem is proved for each type. We then study explicit models which lead to biorthogonal rational functions.Classical Analysis and ODEstext