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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
DOI: https://doi.org/10.1090/S0002-9939-1970-0259412-2
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] O. Perron, Die Lehre von den Kettenbrüchen, Dritte, verbesserte und erweiterte Aufl. Band II: Analytisch-funktionentheoretische Kettenbrüche, Teubner Verlags-gesellschaft, Stuttgart, 1957. MR 19, 25. MR 0085349 (19:25c)
  • [2] A. Magnus, Certain continued fractions associated with the Padé table, Math. Z. 78 (1962), 361-374. MR 27 #272. MR 0150271 (27:272)
  • [3] -, Expansion of power series into $ P$-fractions, Math. Z. 80 (1962), 209-216. MR 27 #273. MR 0150272 (27:273)

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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

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