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A note on rational approximation

Published online by Cambridge University Press:  17 April 2009

C.S. Davis
C.S. Davis
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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Abstract

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It is shown that the inequality

holds for an infinity of integers p, q and that here the factor ½ may not be replaced by a smaller number. Corresponding best possible inequalities are given for the numbers e±2/t, where t is a positive integer.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 3 , June 1979 , pp. 407 - 410
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Davis, C.S., “On some simple continued fractions connected with e”, J. London Math. Soc. 20 (1945), 194–198.Google Scholar
[2]Davis, C.S., “Rational approximations to e”, J. Austral. Math. Soc. Ser. A 25 (1978), 497–502.Google Scholar