Knopfmacher, Arnold; Knopfmacher, John Inverse polynomial expansions of Laurent series. II. (English) Zbl 0684.30030 J. Comput. Appl. Math. 28, 249-257 (1989). An algorithm is given, and shown to lead to various series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by the rational functions which are the partial sums of these series are investigated. The types of series corresponding to rational functions themselves are also partially characterized. The first paper of this sequence appeared in Constructive Approximation 4, 379-389 (1988; Zbl 0659.41024). Reviewer: N.M.Temme Cited in 8 Documents MSC: 30E10 Approximation in the complex plane 30B10 Power series (including lacunary series) in one complex variable 41A25 Rate of convergence, degree of approximation Keywords:series expansions; Laurent series; degrees of approximation Citations:Zbl 0659.41024 PDFBibTeX XMLCite \textit{A. Knopfmacher} and \textit{J. Knopfmacher}, J. Comput. Appl. Math. 28, 249--257 (1989; Zbl 0684.30030) Full Text: DOI References: [1] Baum, L. E.; Sweet, M. M., Continued fractions of algebraic power series in characteristic 2, Ann. of Math., 10, 593-610 (1976) · Zbl 0312.10024 [2] Jones, W. B.; Thron, W. J., Continued Fractions (1980), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0162.09903 [3] Knopfmacher, A.; Knopfmacher, J., Inverse polynomial expansions of Laurent series, Constructive Approximation, 4, 379-389 (1988) · Zbl 0659.41024 [4] Knopfmacher, A.; Knopfmacher, J., A product representation for power series, Complex Variables Theory Appl., 10, 283-294 (1988) · Zbl 0662.30005 [5] Leighton, W.; Scott, W. T., A general continued fraction expansion, Bull. Amer. Math. Soc., 45, 596-605 (1939) · Zbl 0021.33004 [6] Magnus, A., Certain continued fractions associated with the Padé table, Math. Z., 78, 361-374 (1962) · Zbl 0104.05102 [7] Oppenheim, A., The representation of real numbers by infinite series of rationals, Acta Arith., 21, 391-398 (1972) · Zbl 0258.10003 [8] Perron, O., Irrationalzahlen (1951), Chelsea: Chelsea New York · JFM 65.0192.02 [9] Sprindžuk, V. G., Mahler’s Problem in Metric Number Theory, (Trans. Math. Monographs, 25 (1969), Amer. Mathematical Soc: Amer. Mathematical Soc Providence, RI) · Zbl 0287.10043 [10] Zariski, O.; Samuel, P., Commutative Algebra, Vol. 2 (1976), Springer: Springer Berlin · Zbl 0121.27901 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.