On the Divergence in the General Sense of $q$-Continued Fraction on the Unit Circle

Douglas Bowman; James Mc Laughlin

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arXiv · 1812.10873

On the Divergence in the General Sense of $q$-Continued Fraction on the Unit Circle

Douglas Bowman·James Mc Laughlin

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Abstract

We show, for each $q$-continued fraction $G(q)$ in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which $G(q)$ diverges in the general sense. This class includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fraction. We discuss the implications of our theorems for the general convergence of other $q$-continued fractions, for example the G\"{o}llnitz-Gordon continued fraction, on the unit circle.

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Douglas Bowman, James Mc Laughlin. 2018-12-28. On the Divergence in the General Sense of $q$-Continued Fraction on the Unit Circle. https://arxiv.org/abs/1812.10873

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