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On higher order Padé-type approximants with some prescribed coefficients in the numerator

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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References

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Additional information

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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Subject classification

  • AMS (MOS) 33A65

Keywords

  • Padé-type approximants
  • Sobolev-type orthogonal polynomials