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Rational approximations to e

Published online by Cambridge University Press:  09 April 2009

C. S. Davis
C. S. Davis
Affiliation:
University of QueenslandSt. Lucia Brisbane
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Abstract

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The greatest lower bound (in fact, ½) is found of constants k such that for an infinity of rationals p/q.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 4 , June 1978 , pp. 497 - 502
Copyright
Copyright © Australian Mathematical Society 1978

References

Adams, W. W. (1966), “Asymptotic diophantine approxiamtion to e” Proc. Nat. Acad. Sci. U.S.A. 55, 28–31.CrossRefGoogle ScholarPubMed
Bundschuh, P., (1971) “Irrationalitätsmasze für eaa#0 rational oder Liouville-Zahl” Math. Ann. 20, 229–242.CrossRefGoogle Scholar
Davis, C. S. (1945), “On some simple continued fractions connected with e”, J. Lond. Math. Soc. 20, 194–198.CrossRefGoogle Scholar
Euler, L. (1937), “De fractionibus continuis” Comm. Acad. Sc. Imp. Petrop. 9 (Op. Ser. 1, Vol. 14).Google Scholar
Hurwiz, A. (1891), “Ueber die Kettenbruch-Entwicklung der Zahl e” Phys.-ökon, Ges., Königsberg (Werke, Bd. II).Google Scholar
Hurwitz, A. (1896), “Über die Kettenbrü;che, deren Teilnenner arithmetische Reihen bilden” Vierteljahresschrift d. naturforsch. Gesellschaft, Zürich (Werke, Bd. II).Google Scholar
Mahler, K., (1932), “Zur Approximation der Exponentialfunktion und des Logarithmus, I und II,” J. reine angew. Math. 166, 118–136, 137–150.CrossRefGoogle Scholar
Mahler, K. (1953), “On the approximation of п” Proc. Akad. Wetensch. Ser. A 56, 30–42.Google Scholar
Perron, O. (1954). Die Lehre von den Kettenbrüchen., Bd. I, 3. Aufl. (B. G. Teubner, Stuttgart), 123–126.Google Scholar
Perron, O. (1957), Die Lehre von den Kettenbrüchen, Bd. II, 3. Aufl. (B. G. Teubner, Stuttgart), 244–248.Google Scholar
Sundman, K. F. (1895), “Utvecklingarna af e och e2 uti kedhebrak med alla partialtälhare lika met ett” Üfversigt af Finska Vetenskapssocietatens Förhandlingar 38.Google Scholar
Walters, F. C. (1968), “Alternative derivation of some regular continued frations”, J. Aust. Math. Soc. 8, 205–212.CrossRefGoogle Scholar