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The connection between $ P$-fractions and associated fractions


Author: Arne Magnus
Journal: Proc. Amer. Math. Soc. 25 (1970), 676-679
MSC: Primary 40.12
MathSciNet review: 0259412
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Abstract: The associated continued fractions of a power series $ L$ is a special case of the $ P$-fraction of a power series $ {L^{\ast}}$. The latter is closely connected with the Padé table of $ {L^{\ast}}$. We prove that every $ P$-fraction is the limit of the appropriate contraction of associated fractions in the sense that as the coefficients of $ L$ approach those of $ {L^{\ast}}$ the elements and approximants of the contraction approach the elements and approximants of the $ P$-fraction.


References [Enhancements On Off] (What's this?)

  • [1] Oskar Perron, Die Lehre von den Kettenbrüchen. Dritte, verbesserte und erweiterte Aufl. Bd. II. Analytisch-funktionentheoretische Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1957 (German). MR 0085349
  • [2] Arne Magnus, Certain continued fractions associated with the Padé table, Math. Z. 78 (1962), 361–374. MR 0150271
  • [3] Arne Magnus, Expansion of power series into 𝑃-fractions, Math. Z. 80 (1962), 209–216. MR 0150272

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0259412-2
Keywords: Continued fractions, associated continued fractions, $ P$-fractions, Padé table
Article copyright: © Copyright 1970 American Mathematical Society