Abstract
It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arbitrary prescribed real or complex conjugate poles. The number of terms in the recursion relation is shown to be related to the structure of the orthogonal rational functions.
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Acknowledgments
We would like to thank Bernardo de la Calle Ysern, Leonid Knizhnerman, Paco Marcellan, and an anonymous referee for comments.
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M. S. Pranić’s Research supported in part by the Serbian Ministry of Education and Science (Research Project: “Methods of numerical and nonlinear analysis with applications” (No. #174002)). L. Reichel’s Research supported in part by NSF grant DMS-1115385.
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Pranić, M.S., Reichel, L. Recurrence relations for orthogonal rational functions. Numer. Math. 123, 629–642 (2013). https://doi.org/10.1007/s00211-012-0502-8
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DOI: https://doi.org/10.1007/s00211-012-0502-8