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

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 Göllnitz-Gordon continued fraction, on the unit circle.

25 pages

References in corpus (2)

• The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle
• A Theorem on Divergence in the General Sense for Continued Fractions