On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle

91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.General convergence is a concept introduced by Lisa Lorentzen (nee Jacobson) and is stronger in the sense that classical convergence implies general convergence. We show that all continued fractions in a certain class, which includes the Rogers-Ramanujan continued fractions and the three "Ramanujan-Selberg" continued fractions, diverge in the general sense at an uncountable set of points on the unit circle. We also show that the Rogers-Ramanujan continued fraction converges generally at all roots of unity (in contrast to classical convergence) and that it does not converge generally at any point outside the unit circle.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD