Analytic Theory of Continued Fractions III: Proceedings of a by S. Clement Cooper (auth.), Lisa Jacobsen (eds.) PDF

By S. Clement Cooper (auth.), Lisa Jacobsen (eds.)

ISBN-10: 354046820X

ISBN-13: 9783540468202

ISBN-10: 3540518304

ISBN-13: 9783540518303

Contents: S.C. Cooper: -Fraction ideas to Riccati Equations.- R.M. Hovstad: Irrational endured Fractions.- L. Jacobsen, W.J. Thron, H. Waadeland: Julius Worpitzky, his Contributions to the Analytic conception of endured Fractions and his Times.- W.B. Jones, N.J. Wyshinski: confident T-Fraction Expansions for a relatives of distinct Functions.- J.H. McCabe: On persevered Fractions linked to Polynomial variety Padé Approximants, with an Application.- O. Njastad: Multipoint Padé Approximants and similar persisted Fractions.- O. Njastad: A Survey of a few effects on Separate Convergence of persisted Fractions.- O. Njastad, H. Waadeland: a few feedback on Nearness difficulties for endured Fraction Expansions.- W.J. Thron: endured Fraction Identities Derived from the Invariance of the Crossratio lower than Linear Fractional Transformations.- H. Waadeland: Boundary types of Worpitzky's Theorem and of Parabola Theorems.

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Additional info for Analytic Theory of Continued Fractions III: Proceedings of a Seminar-Workshop, held in Redstone, USA, June 26–July 5, 1988

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Bayrische Akademie, Dunker und Humblot, M~inchen 1875-1912 and the "Neue Deutsche Biographie" Bayrische Akademie, vol. t (1952) - vol. 15 (1986), Dunker und Humblot, Berlin. Biographies and other historical articles in the "Jahresberichte der DMV" also proved helpful. A great deal of our information about UB was obtained from: Kurt R. Biermann, "Die Mathematik und ihre Dozenten an der Berliner Universitlit, 1810-1920", Akademie Verlag, Berlin 1973. B. L. Butzer, F. , pp. 42-51, Birkh/iuser Verlag, Basel 1981 provided many facts about that institution.

Bell among others) t h a t m a t h e m a t i c a l results published in secondary school reports are not likely to a t t r a c t attention. This proved to be the case for Worpitzky's theorem, but there are numerous reasons why a different outcome could have been expected. M a t h e m a t i c a l research had appeared in annual publications of secondary schools before '65. Both K u m m e r and Weierstrass had made use of 42 these outlets for some of their results. Beginning with the mathematical results published in '68 the Jahrbuch fiber die Fortschritte der Mathematik set out to review all published mathematical research.

He corrected this oversight in the printed pamphlet. It seems likely t h a t Worpitzky sent a manuscript of his results to Grunert and possibly the other two. If so, it is surprising t h a t none of them mentioned the earlier work of Lagrange and Euler. One also wonders whether the errors which Worpitzky made in the paper were noticed. Using modern terminology we can set ax m Sn(w) = 1 + . ax m . m+l = . 1) and w n is a solution of a related differential equation. 4) xy = lim fn = lim Sn(0) . 4).

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Analytic Theory of Continued Fractions III: Proceedings of a Seminar-Workshop, held in Redstone, USA, June 26–July 5, 1988 by S. Clement Cooper (auth.), Lisa Jacobsen (eds.)


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