arXiv math/94072131994-07-20math.CA

Generalized orthogonality and continued fractions

Mourad E. H. Ismail, David R. Masson

英文摘要：

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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