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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C. Brezinski,Padé-Type Approximation and General Orthogonal Polynomials, ISNM vol. 50 (Birkhäuser, Basel, 1980).
C. Brezinski, Partial Padé approximation, J. Approx. Theory 54 (1988) 210–233.
F. Marcellán and A. Ronveaux, On a class of polynomials orthogonal with respect to a Sobolev inner product, Indag. Math. N.S. 1 (1990) 451–464.
G. Pólya and G. Szegö,Problems and Theorems in Analysis II (Springer, 1954).
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
- AMS (MOS) 33A65
- Padé-type approximants
- Sobolev-type orthogonal polynomials