A theorem on $T$-fractions corresponding to a rational function
Author:
Kari Hag
Journal:
Proc. Amer. Math. Soc. 25 (1970), 247-253
MSC:
Primary 30.25
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259081-1
MathSciNet review:
0259081
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Abstract | References | Similar Articles | Additional Information
Abstract: We prove that a limitärperiodisch $T$-fraction, which corresponds to a rational function, has the property that ${d_n} \to - 1$.
- W. J. Thron, Some properties of continued fractions $1+d_0z+K(z/(1+d_n z))$, Bull. Amer. Math. Soc. 54 (1948), 206–218. MR 24528, DOI https://doi.org/10.1090/S0002-9904-1948-08985-6
- 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
- Walter Leighton and W. T. Scott, A general continued fraction expansion, Bull. Amer. Math. Soc. 45 (1939), 596–605. MR 41, DOI https://doi.org/10.1090/S0002-9904-1939-07046-8
- Arne Magnus, Certain continued fractions associated with the Padé table, Math. Z. 78 (1962), 361–374. MR 150271, DOI https://doi.org/10.1007/BF01195180
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Keywords:
<IMG WIDTH="20" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$T$">-fraction expansion,
limitärperiodisch <IMG WIDTH="20" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$T$">-fraction,
continued fractions,
power series
Article copyright:
© Copyright 1970
American Mathematical Society