Generalized orthogonality and continued fractions

Details Generalized orthogonality and continued fractions Generalized orthogonality and continued fractions

1994-07-20

arxiv.org/abs/math/9407213v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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