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Some properties of the continued fraction expansion of (m/n) e1/q

Published online by Cambridge University Press:  24 October 2008

K. R. Matthews  and
R. F. C. Walters
K. R. Matthews
Affiliation:
University of Queensland, Australia
R. F. C. Walters
Affiliation:
University of Queensland, Australia
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Extract

Introduction. Continued fractions of the form are called Hurwitzian if b1, …, bh, are positive integers, ƒ1(x), …, ƒk(x) are polynomials with rational coefficients which take positive integral values for x = 0, 1, 2, …, and at least one of the polynomials is not constant. f1(x), …, fk(x) are said to form a quasi-period.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 67 - 74
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Davis, C. S.On some simple continued fractions connected with e. J. London Math. Soc. 20 (1945), 194–198.CrossRefGoogle Scholar
(2)Kolden, K.Continued fractions and linear substitutions. Arch. Math. Naturvid.. 50 (1949), 141–196.Google Scholar
(3)Lehmeb, D. N.Arithmetical theory of certain Hurwitzian continued fractions. Amer. J. Math. 40 (1918), 375–390.CrossRefGoogle Scholar
(4)Perron, O.Die Lehre von den Kettenbrüchen. Bd. 1, 110–123. (3rd ed.Teubner, 1954.)Google Scholar
(5)Waiters, R. F. C.Alternative derivation of some regular continued fractions. J. Austral. Math. Soc. 8 (1968), 205–212.CrossRefGoogle Scholar