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arXiv · 2004.06350

Study of the transcendence of a family of generalized continued fractions

Túlio O. Carvalho
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Abstract

We study a family of generalized continued fractions, which are defined by a pair of substitution sequences in a finite alphabet. We prove that they are stammering sequences, in the sense of Adamczewski and Bugeaud. We also prove that this family consists of transcendental numbers which are not Liouvillian. We explore the partial quotients of their regular continued fraction expansions, arriving at no conclusion concerning their boundedness.

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Túlio O. Carvalho. 2020-04-14. Study of the transcendence of a family of generalized continued fractions. https://arxiv.org/abs/2004.06350

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