On the Convergence of Limit Periodic Continued Fractions K (an/1) where an ... 1/4. Part IV

Lorentzen, Lisa
January 2002
Constructive Approximation;2002, Vol. 18 Issue 1, p1
Academic Journal
Continued fractions K (a[SUBn]/B[SUBn]), where a[SUBn], b[SUBn] &epsis; C and a[SUBn]/b[SUBn]b[SUBn-1] ? -� may converge or diverge depending on how a[SUBn]/b[SUBn]b[SUBn-1] approaches its limit. Due to equivalence transformations it suffices to study the special case where all b[SUBn] = 1. We shall prove that K (a[SUBn]/1) converges if a[SUBn] ? -� and there exists a set V ? C ? {8} with certain properties such that a[SUBn]/(1 + V) ? V for all n. We shall also summarize some other useful consequences of such value sets V.


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