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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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.

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