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Title:On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle
Author(s):Mc Laughlin, James
Doctoral Committee Chair(s):Douglas Bowman
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:2002
Type:Text
Language:English
Description:91 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.
URI:http://hdl.handle.net/2142/86801
Other Identifier(s):(MiAaPQ)AAI3070383
Date Available in IDEALS:2015-09-28
Date Deposited:2002


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