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A series and its associated continued fraction


Author: J. L. Davison
Journal: Proc. Amer. Math. Soc. 63 (1977), 29-32
MSC: Primary 10F35
DOI: https://doi.org/10.1090/S0002-9939-1977-0429778-5
MathSciNet review: 0429778
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Abstract: Let $ \alpha = (1 + \surd 5)/2$. In this paper it is proved that

$\displaystyle [unk]$

where $ {t_n} = {2^{{f_{n - 2}}}}$ and $ ({f_n})$ is the Fibonacci sequence. It is also shown that $ T(\alpha )$ is transcendental.

References [Enhancements On Off] (What's this?)

  • [1] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Math. and Math. Phys., no. 45, Cambridge Univ. Press, London and New York, 1957. MR 19, 396. MR 0087708 (19:396h)
  • [2] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 3rd ed., Clarendon Press, Oxford, 1954. MR 16, 673. MR 0067125 (16:673c)
  • [3] K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20; Corrigendum, 168. MR 17, 242. MR 0072182 (17:242d)

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DOI: https://doi.org/10.1090/S0002-9939-1977-0429778-5
Article copyright: © Copyright 1977 American Mathematical Society

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