Continued fractions for some alternating series

@article{Davison1991ContinuedFF,
  title={Continued fractions for some alternating series},
  author={J. Davison and J. Shallit},
  journal={Monatshefte f{\"u}r Mathematik},
  year={1991},
  volume={111},
  pages={119-126}
}
AbstractWe discuss certain simple continued fractions that exhibit a type of “self-similar” structure: their partial quotients are formed by perturbing and shifting the denominators of their convergents. We prove that all such continued fractions represent transcendental numbers. As an application, we prove that Cahen's constant $$C = \sum\limits_{i \geqslant 0} {\frac{{( - 1)^i }}{{S_i - 1}}}$$ is transcendental. Here (Sn) isSylvester's sequence defined byS0=2 andSn+1=Sn2−Sn+1 forn≥0. We also… Expand

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