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The classical irrationality problem for  -fractions
Author:
R. M. Hovstad
Journal:
Proc. Amer. Math. Soc. 110 (1990), 65-70
MSC:
Primary 40A15; Secondary 11J70, 11J72, 41A21
MathSciNet review:
1017002
Full-text PDF Free Access
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Additional Information
Abstract: Necessary and sufficient conditions are given for a  -fraction to correspond to a rational function.
- [1]
Kari
Hag, A theorem on 𝑇-fractions
corresponding to a rational function, Proc.
Amer. Math. Soc. 25
(1970), 247–253. MR 0259081
(41 #3723), http://dx.doi.org/10.1090/S0002-9939-1970-0259081-1
- [2]
Kari
Hag, A convergence theorem for
limitärperiodisch 𝑇-fractions of rational functions,
Proc. Amer. Math. Soc. 32 (1972), 491–496. MR 0291421
(45 #514), http://dx.doi.org/10.1090/S0002-9939-1972-0291421-1
- [3]
T. H. Jefferson, Some additional properties of
 -fractions, Ph. D. thesis, University of Colorado, Boulder, Colorado, 1969.
- [4]
William
B. Jones and Wolfgang
J. Thron, Continued fractions, Encyclopedia of Mathematics and
its Applications, vol. 11, Addison-Wesley Publishing Co., Reading,
Mass., 1980. Analytic theory and applications; With a foreword by Felix E.
Browder; With an introduction by Peter Henrici. MR 595864
(82c:30001)
- [5]
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 (19,25c)
- [6]
-, Die Lehre von den Kettenbrüchen, Band I, 3. Aufl, Teubner, Stuttgart, 1954.
- [7]
H. Waadeland, Some properties of general
 -fractions, Univ. i Trondheim, Matematisk Institutt (NLHT), Trondheim, 1978.
- [8]
Haakon
Waadeland, Tales about tails, Proc. Amer. Math. Soc. 90 (1984), no. 1, 57–64. MR 722415
(85f:40003), http://dx.doi.org/10.1090/S0002-9939-1984-0722415-5
- [9]
-, General
 -expansions of bounded functions, Dept. of Math., Trondheim, no. 2, 1983.
- [1]
- K. Hag, A theorem on
 -fractions corresponding to a rational function, Proc. Amer. Math. Soc. 25 (1970), 247-253. MR 0259081 (41:3723)
- [2]
- -, A convergence theorem for Limitärperiodisch
 -fractions of rational functions, Proc. Amer. Math. Soc. 32 (1972), 491-496. MR 0291421 (45:514)
- [3]
- T. H. Jefferson, Some additional properties of -fractions, Ph. D. thesis, University of Colorado, Boulder, Colorado, 1969.
- [4]
- W. B. Jones and W. J. Thron, Continued fractions, Analytic theory and applications, Addison-Wesley, Reading, MA, 1980. MR 595864 (82c:30001)
- [5]
- O. Perron, Die Lehre von den Kettenbrüchen, Band II, 3. Aufl., Teubner, Stuttgart, 1957. MR 0085349 (19:25c)
- [6]
- -, Die Lehre von den Kettenbrüchen, Band I, 3. Aufl, Teubner, Stuttgart, 1954.
- [7]
- H. Waadeland, Some properties of general -fractions, Univ. i Trondheim, Matematisk Institutt (NLHT), Trondheim, 1978.
- [8]
- -, Tales about tails, Proc. Amer. Math. Soc. 90 (1984), 57-64. MR 722415 (85f:40003)
- [9]
- -, General -expansions of bounded functions, Dept. of Math., Trondheim, no. 2, 1983.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1017002-0
PII:
S 0002-9939(1990)1017002-0
Article copyright:
© Copyright 1990 American Mathematical Society
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