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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 | References | Similar Articles | Additional Information

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.


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Keywords: Continued fractions, associated continued fractions, <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$P$">-fractions, Pad&#233; table
Article copyright: © Copyright 1970 American Mathematical Society