New PDF release: Analytic Theory of Continued Fractions: Proceedings of a

By William B. Jones, W. J. Thron, Haakon Waadeland (eds.)

ISBN-10: 3540115676

ISBN-13: 9783540115670

ISBN-10: 3540392769

ISBN-13: 9783540392767

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Extra resources for Analytic Theory of Continued Fractions: Proceedings of a Seminar-Workshop held at Loen, Norway, 1981

Sample text

21) ~(n) = FI/G I and ~(n) > 0 for i < j < n j=l J ~ 3 (A) and (B) are Immediate consequences of Theorems Proof. 3 [13, Theorem in Section . 5. system of three-term G n > 0 r for all E ~(0,~) with respect Proof. la) . If there theorem is also a partial recurrence to r be any sequence An(Z) {Qn(Z)}0 denominator, respectively [ii, p. la) formula to each other problem , corresponds ~ , respectively. 3(B) a distribution F and decomposition for classical of the form there exists normalized The numbers of Theorem of a theorem relations Then fraction [3] .

Thron and H. Waadeland, A strong StieltJes moment problem, Trans. Amer. Math. , (1980), 503-528. 14. , 19 (1895), pp. 93-104. 15. Meyer, Burnett, On continued fractions corresponding submitted. 16. H. A. Murphy, Continued fractions which correspond to power series expansions at two points, ~. Maths. A~plics. 17 (1976), 233-247. 17. , Die Lehre von den Kettenbr~chen, (1957). 18. A. , An algorithm for Gaussian quadrature given modified moments, Numer. Math. 18 (1971/72), 465-478. 19. , Quelques recherches sur la theorie des quadratures mechanlques, Ann.

2) . 3) . lb) . 15) that Bn(Z ) denote the positive nth T-fractlon m = 0,1,2,... 5) . 16) Vn(Z) and of the corresponding J=l z + ~ n) has the same form as , An(Z) n = 1,2,3,... 1 and Pn(t~n)) = w~ n) . 2. 1 . 17) F(t) for which the Riemann-Stieltjes integral on the exists. 2 . It is the analogue of a theorem of Markoff [14] . 3. Let ~(t) E~(a,b) with 0 < a < b < +~ . 18) (B) coefficients zS b d~(t) a z+t The positive every compact subset by the integral Proof. 4. 18) (A): = defined ... 18) converges to the holomorphic uniformly function on defined .

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Analytic Theory of Continued Fractions: Proceedings of a Seminar-Workshop held at Loen, Norway, 1981 by William B. Jones, W. J. Thron, Haakon Waadeland (eds.)


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