Generalized Orthogonality and Continued Fractions Original Research Article

The connection between continued fractions and orthogonality which is familiar for J-fractions and T-fractions is extended to what we call R-fractions of types 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.