A series and its associated continued fraction
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- by J. L. Davison PDF
- Proc. Amer. Math. Soc. 63 (1977), 29-32 Request permission
Abstract:
Let $\alpha = (1 + \surd 5)/2$. In this paper it is proved that \[ [unk]\] where ${t_n} = {2^{{f_{n - 2}}}}$ and $({f_n})$ is the Fibonacci sequence. It is also shown that $T(\alpha )$ is transcendental.References
- J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
- K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1–20; corrigendum, 168. MR 72182, DOI 10.1112/S0025579300000644
Additional Information
- © Copyright 1977 American Mathematical Society
- 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