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On the Convergence of Limit Periodic Continued Fractions K(an/1) where an→ - ¼. Part IV
Authors:Lisa Lorentzen
Institution:(1) Department of Mathematics Norwegian University of Science and Technology N—7491 Trondheim Norway, NO
Abstract:Continued fractions K(a n /b n ) , where a n , b n \smallbf C and a n /b n b n-1 →-\frac 14 , may converge or diverge depending on how a n /b n b n-1 approaches its limit. Due to equivalence transformations it suffices to study the special case where all b n =1 . We shall prove that K(a n /1) converges if a n →-\frac 14 and there exists a set V\subseteq\smallbf C \cup{∈fty} with certain properties such that a n /(1+V)\subseteq V for all n . We shall also summarize some other useful consequences of such value sets V . January 31, 2000. Date revised: July 28, 2000. Date accepted: August 16, 2000.
Keywords:, Parabolic limit periodic continued fractions, Convergence, Divergence, Value sets, AMS Classification, 40A15,
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