Download e-book for iPad: Analytic Theory of Continued Fractions II: Proceedings of a by Christopher Baltus, William B. Jones (auth.), Wolfgang J.

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

Example text

All p o s s i b l e that all E values is are something about how to which n-values decide fast an + -T ... g. list of given. "naive" E the several fraction. information E(N) re$ion. av aI a2 K (-]-) = -~- + -]- + ~:I = all p o s s i b l e The of an[{, ' contained in a d v a n c e , converges, W, references ... 2) set all fractions We w o u l d I of a c e r t a i n that which will the a ~ + continued finite. 1) values following: approach with fn' w h e r e N be to c h o o s e a finite, elements, would and fixed a n £ E(N).

34 (1980), 11. , (1984), 57-64. , Die 1957. , Even and to a p p e a r in J. Odd Parts CAM. of Limit W. , Continued Fractions: Analytic Encyclopedia of Math. , Uber die Konvergenz unendlicher A k a d . W i s s . M a t h . - Nat. K!. , On Parabolic Math. Zeitschr. 69 Convergence Regions (1958), 1 7 3 - 1 8 2 . II, B. G. Kettenbruche, 295-324. for Continued 155-170. Tales about Tails, Proc. Amer. Math. Soc. 90 O N SIMPLE C O N V E R G E N C E R E G I O N S FOR C O N T I N U E D F R A C T I O N S K(an/1) A THEOREM Lisa J a c o b s e n D e p a r t m e n t of M a t h e m a t i c s and S t a t i s t i c s The U n i v e r s i t y of T r o n d h e i m AVH N-7055 Dragvoll, Norway I.

2] is tails called tails of K ( a n / l ) or N=1,2,3 ..... 3] K(an/1), complex a sequence K(an/l) of if of riaht or or not. they diverges [11]. 22, n view f(N) tall convergence/divergence = aN/( I + f(N)), regardless tails known axis. a N E R U to p r o v e {g(n)}~=0 a sequence converges, [I0]. ' sequence sequence always [7 S a t z shall if its N t h are not [11]. Results. Let Then is of K ( a n / 1 ) , called + suffices = S N ( f(N) ), f (N-I) {f(N)} the sequence 3. if a n d o n l y Then every satisfying wronu it We K(an/l ) converges.

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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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