Abstract
In this work, we consider the construction of higher order rational approximants to a formal power series, with some prescribed coefficients in their numerators, precisely those of the higher order powers. The denominators of such approximants are related to the so-called Sobolev-type orthogonal polynomials. The elementary properties of these orthogonal polynomials are studied in the regular case.
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This research was partially supported by Junta de Andalucía, Grupo de Investigación 1107.
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Piñar, M.A., Pérez, T.E. On higher order Padé-type approximants with some prescribed coefficients in the numerator. Numer Algor 3, 345–352 (1992). https://doi.org/10.1007/BF02141942
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DOI: https://doi.org/10.1007/BF02141942