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

Example text

7]) are of other the entries in rows. APT-fraction the first row. 2] leading that = Mn,l(Z) Theorem we see ~ 0 for ~(-n+2) n rO-n and hence entry in We for = (-1) we that coefficients, H(-n+l)(C)n @n for ii n = i, showed $O$n ~ 0 1, 2, ... the (where respectively, n = 2 .... that $0 = are n the Bn(Z) ) . 1] , we we see have (C) Therefore, by Lemma 7, given Hin2n+l)(c) (2) " (-(2n+l)) n2n+l (C) (3) N ( - 2 n ) (C) --2n+1 > 0 (4) H~n2n) (C) > 0 i, (z)) H(-n+I)(c) n (1) n = 0, and n Sn of H(-n+2)(C) ~ 0 f o r n = I, 2 .....

1] [6]). 2] m=O by C. 2, > is In fLs SSMP shown that in occur as THEOREM 9. ) with = ~. It positive and L (C) of the Under C, namely T-fraction z a could generated {Cn}n=_ a positive with a pair fLs 2 we associated L(C) for start can a pair and M-table 0 We Definition determinants and the such to { - C _ n } n = _ ~, here. 7]} = n = b~-infinite satisfyinq = n. Lo(C) Also, that C the in at the n = since i, Gn the deg(Bn(Z)) = O(z n+i) - An(Z) Bn(Z)L - An(Z ) = O_(zO). (C) satisfies th which will be T-fraction and that i, 2, this ...

2 we the c o e f f i c i e n t s that the h y p o t h e s i s reach Definition and 4k under order exists Thus, - u p to a c o n s t a n t In From Ak nonzero solution ~n a H ( - n + k + l ) ( c ) (-1, F 0 _ n (-1)n@0H n ~n ~ O. 1] [6]). 2] m=O by C. 2, > is In fLs SSMP shown that in occur as THEOREM 9. ) with = ~. It positive and L (C) of the Under C, namely T-fraction z a could generated {Cn}n=_ a positive with a pair fLs 2 we associated L(C) for start can a pair and M-table 0 We Definition determinants and the such to { - C _ n } n = _ ~, here.

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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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