Download Analytic Theory of Continued Fractions II: Proceedings of a by Christopher Baltus, William B. Jones (auth.), Wolfgang J. PDF

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By Christopher Baltus, William B. Jones (auth.), Wolfgang J. Thron (eds.)

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Extra resources for Analytic Theory of Continued Fractions II: Proceedings of a Seminar-Workshop held in Pitlochry and Aviemore, Scotland June 13–29, 1985

Example text

G ~ E E ~ ~. is a limit re@ion be an open connected subset of a bounded p r e - v a l u e re ion G region in many cases a severe restriction. contain at least two points. 2. conditions is E/(I+W) ~ W, We shall prove the following Theor@m E; that regions can be regarded as value regions for m o d i f i e d Sn(W) for continued for introduced by Thron Please observe Such pre-value W for Let E. ~, and let W Then every finitely connected, is such that G b__ee open is a conver@ence re@ion. The proofs of these results are found in Section we extend these results to twin regions.

Cn)n=_~, such and the Furthermore, related. as when T-fraction moments, numbers that C_m zm Stronu find increasing increase - z = ~. stated = shown m=l positive we real be C monotonically points have and again can ~ • intimately sequence problem hence we the (C) M-table Once H ( - ( n - k ) ) (C) n normal. Lo(C) z = 0 and you established ... _ . we +1, for argument 1, does function that for (n = O, there exist ~(t) each ±i, on (-~, n, ± 2 .... )? a real-valued, ~) with bounded, infinitely many 33 In [5], Jones and Thron showed that if C s a t i s f i e s the c o n d i t i o n H ( - 2 n ) ( c ) > 0 and H ( - 2 n ) ( c ) > 0 for n = O, 1 ....

On page 44 the element real axis, region with and the b o u n d a r y On page 45 2w -~- , still observe constant to the right with that to the half radius. 6). values region, the the closed on the ray to a circle (limit) on the p o s i t i v e by m o v i n g of the "tends" of the is c e n t e r e d values region radius. 7). we equal 44 On p a g e region. 6), as , now with element both region. SO RO ) a = 14 + 2 , / - 5 c=4, 0 5-V'5 2 = -~,$0 Im ~ ! 98... 01... e|. 2SIIllI • ... describing ".. ,..................

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