On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle
Mc Laughlin, James
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https://hdl.handle.net/2142/86801
Description
Title
On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle
Author(s)
Mc Laughlin, James
Issue Date
2002
Doctoral Committee Chair(s)
Douglas Bowman
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
"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."
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