Generalized orthogonality and continued fractions
Classical Analysis and ODEs
2008-02-03 v1
Abstract
The connection between continued fractions and orthogonality which is familiar for -fractions and -fractions is extended to what we call -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.
Cite
@article{arxiv.math/9407213,
title = {Generalized orthogonality and continued fractions},
author = {Mourad E. H. Ismail and David R. Masson},
journal= {arXiv preprint arXiv:math/9407213},
year = {2008}
}