Generalized orthogonality and continued fractions
Mourad E. H. Ismail, David R. Masson
Abstract
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 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.
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