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

ISBN-10: 3540167684

ISBN-13: 9783540167686

ISBN-10: 3540388176

ISBN-13: 9783540388173

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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

Sample text

All n = The periodic where Sec. converges {~}. fractions limit sequence an + -'[' ... 43] poles of the limit < no and ~ @ on ~ = ~ how the continued @n z approaches [1, 4, 9]. In continued th~s paper fractions we shall K(an/1 ) prove where a divergence an ~ -1/4. theorem This for may a family seem of very 49 special, since @ ~ O, ~, in [6, it and Sec. 3] the limit with ~ ~ if examples function. ~, and let If + $ 2 n )z ~ 0 f o r K(~nZ/l); {g2n(Z)}n=l,_ the z of a p p r o x l m a n t s . (~2n-I of for point n = 2, is, a 3, 4 ....

6] < ~. 2. 5] conditions K(an/1) is a wrong tails right tails g(n) real satisfying since just the tails for K ( a n / l ). 5]. to equivalent real can whereas = -i + a n / g ( n - l ) a requiring sequence not be g(0) where an a {g(n)} of sequence of ( ~. ) (ii) We c o u l d (ill) continued ~ O, ~ s i n c e g(n) Im g(n) are require conjugates in S e c t i o n (Im g ( n ) ) / ( R e (~(n)} are 2, it s u f f i c e s g(n)) also < 0 for all a sequence n, of w r o n g that a tail of K ( a n / l ) the c o n d i t i o n s .

Of continued fractions. J. of ON THE a ~ n CONVERGENCE -1/4. PART OF LIMIT is A previous generalized. an -1/4 = lel We (c _ + = O(1/logan), 1. e a an aI 1 FRACTIONS K(an/1), WHERE Statistics divergence criterion show K(an/l ) n) that /n(n + 1) A Continued a2 + and AVH 1 by where , A. Magnus diverges c and (by > the author oscillation) 1/16 and en if ~ > 2. Introduction: K" 1 CONTINUED II Lisa Jacobsen Department of M a t h e m a t i c s University of T r o n d h e i m , N-7055 Dragvoll Norway Abstract.

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Analytic Theory of Continued Fractions II: Proceedings of a Seminar-Workshop held in Pitlochry and Aviemore, Scotland June 13–29, 1985 by Christopher Baltus, William B. Jones (auth.), Wolfgang J. Thron (eds.)


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