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¨ollnitz-Gordon continued fraction, on the unit circle.
Communications in the Analytic Theory of Continued Fractions
Colorado Mesa University
Bowman, D., & McLaughlin, J. (2003). On The Divergence in the General Sense of q-Continued Fractions on the Unit Circle. Communications in the Analytic Theory of Continued Fractions, 11, 25-49. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/42