By Christopher Baltus, William B. Jones (auth.), Wolfgang J. Thron (eds.)
Read Online or Download Analytic Theory of Continued Fractions II: Proceedings of a Seminar-Workshop held in Pitlochry and Aviemore, Scotland June 13–29, 1985 PDF
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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
I, (C) From ±2, is the ... We normal if definition will show H(-(n+k))(C) ~ 0, n k a n d t h e n o n -k. identity l we see i, 2 .... 2, ' ""' and 2, " (C) We -( 2m( +2 1m+1))(C) M 2(m-+(l( 2 m + l ) + 2 k ) ) ( C ) > O, begin < 0 by by pointing (3) ' f o r m = < 0 out that 1 ' 2 ' ... that 2 = H ((_ ( 2 mC+ l ) )) ( C )2 H ~ m- (m2 m _ l ) ) 2m+l = O, H ~m (2m+(2k+l))) > O, _ H(-(2m+l)) for m = H(-((2m+l)+(2k+l)))(C) > 0 2m+1 O, 1, 2 ..... m = O, 1, 2 .... H(-2m)(C)2m Using n ' > 0 . = . 1. 2 .
9. Thron, W. Fractions, i0. T h r o n , W. J. , A c c e l e r a t i n g Convergence of L i m i t Periodic Continued Fractions K(an/l), Numer. Math. 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.
J=O that ISN(O) for *j)l exp(2i j=N+I I. 141 and either the This wrong Hence, N m. That oscillates tail is, or c o n v e r g e s K(al+n/l) of to a c o n t r a d i c t i o n for K(al+n/1), oscillates {Sn(O)} Cauchy converges to {g(l+n) }n=O is since we no to ~. 6] is can repeat the d o e s not hold. Q Unfortunately {g(n) ) rather the c o n d i t i o n s than continued fractions conditions since on {an). 2] show that satisfy tails the the 53 g(n) of = _ --1 _ 1/4 + i~/c - 1 / 1 6 , 2 n + p + 1 wrong tails.
