Analytic Theory of Continued Fractions: Proceedings of a by William B. Jones, W. J. Thron, Haakon Waadeland (eds.)

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

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

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Ii. Jones, William B. J. Thron, Continued Fractions: Anal~tic Theory and A~lications, Encyclopedia of Mathematics and Its Applications, No. ii, Addison-Wesley Publishing Company, Reading, Mass. (1980). 12. Jones, William B. J. E. P. ), 13. J. 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, ~.

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] . {Qn(Z)}; n > i . 3 . 1 ... 1) to formal by . 16) , by comparing satisfied by the Vn(Z) .

13) n (B) r~. j ) J we first show that Pn(Z) = zf b Qn(Z)~n(t)d~(t) a z-t , n = 0,1,2,... 2) . 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.

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