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arXiv · 1812.11219

The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle

Douglas Bowman·James Mc Laughlin
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Abstract

We consider two classes of $q$-continued fraction whose odd and even parts are limit 1-periodic for $|q|>1$, and give theorems which guarantee the convergence of the continued fraction, or of its odd- and even parts, at points outside the unit circle.

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Douglas Bowman, James Mc Laughlin. 2018-12-28. The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle. https://doi.org/10.1216/rmjm/1181069430

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