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

"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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Mc Laughlin, James

Contributors dc:contributor

• Douglas Bowman

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3070383

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86801