In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a wider class of qcontinued fractions, a class which includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fractions. We show, for each q-continued fraction, G(q), in this class, that there is an uncountable set of points, YG, on the unit circle such that if y ∈ YG then G(y) does not converge to a finite value. We discuss the implications of our theorems for the convergence of other q-continued fractions, for example the G¨ollnitz-Gordon continued fraction, on the unit circle.
The Ramanujan Journal
Bowman, D., & McLaughlin, J. (2006). The Convergence behavior of q-Continued Fractions on the Unit Circle. The Ramanujan Journal, 12(2), 185-195. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/64