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A remarkable class of continued fractions

Authors: William W. Adams and J. L. Davison
Journal: Proc. Amer. Math. Soc. 65 (1977), 194-198
MSC: Primary 10F35
MathSciNet review: 0441879
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Abstract: For any irrational number $ \alpha $ and integer $ a > 1$, the continued fraction of $ (a - 1)\sum _{r = 1}^\infty 1/{a^{[r\alpha ]}}$ is computed explicitly in terms of the continued fraction of $ \alpha $.

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

  • [1] J. W. S. Cassels, An introduction to diophantine approximations, Cambridge Univ. Press, Cambridge, 1957. MR 0087708 (19:396h)
  • [2] J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), 29-32. MR 0429778 (55:2788)
  • [3] S. Lang, Introduction to diophantine approximations, Addison-Wesley, Reading, Mass., 1966. MR 0209227 (35:129)
  • [4] J. H. Loxton and A. J. Van der Poorten, Arithmetric properties of certain functions of several variables. III, Bull. Austral. Math. Soc. 16 (1977), 15-49. MR 452125 (81g:10046)
  • [5] -, Transcendence theory: Advances and applications, Academic Press, New York, 1977, pp. 211-226.

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