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Proceedings of the American Mathematical Society

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

 
 

 

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.


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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