Get Analytic Theory of Continued Fractions III: Proceedings of a 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 recommendations to Riccati Equations.- R.M. Hovstad: Irrational persisted Fractions.- L. Jacobsen, W.J. Thron, H. Waadeland: Julius Worpitzky, his Contributions to the Analytic conception of persevered Fractions and his Times.- W.B. Jones, N.J. Wyshinski: confident T-Fraction Expansions for a family members of precise Functions.- J.H. McCabe: On persisted Fractions linked to Polynomial style 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 persevered Fractions.- O. Njastad, H. Waadeland: a few feedback on Nearness difficulties for endured Fraction Expansions.- W.J. Thron: persisted Fraction Identities Derived from the Invariance of the Crossratio less than Linear Fractional Transformations.- H. Waadeland: Boundary models 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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In 1905, or shortly before then, someone brought Worpitzky's article to the attention of Van Vleek (himself a rediseoverer of the theorem) who then acknowledged Worpitzky's priority in his "Selected Topics in the Theory of Divergent Series and of Continued Fractions" in the "Boston Colloquium". Van Vleck thought t h a t the paper was Worpitzky's dissertation which makes it likely t h a t he never saw the article itself. E. W~lffing in his 1908 article "Wer hat iiber Kettenbriiehe gearbeitet", 26 which is simply a list of publications on continued fractions, has a reference to Worpitzky.

2) converges uniformly on every compact subset of D ( a , b ) : = { z : z Lo = Lo(z) = q~ [ - b , - a } } to G(z). 4) j=0 axe asymptotic power series expansions of G(z) at z = 0 and z = oo, respectively, with respect to the sectors R,, = {z : [Arg z[ < a , 0 < c~ < 7r}. That is, for each m = 1 , 2 , 3 , - . , [G ( z ) z-" - L0,,~(z) • : O(~), z .... 5~) where Lo,rn::~-~-c_jzJ~ j=l and L o a , m : = ~ c j z -i. 6) where the symbol h 0 ( f ) (Aoo(f)) denotes the Taylor (Laurent) series expansion of f about z = 0 (z = oo).

He completed his studies at the University of Berlin in the winter semester 1857/8. T h e city of Greifswald was settled around 1240 by people coming from the Netherlands. It became a member of the Hanseatic League in 1278. The university was founded in 1456. From 1648 to 1815 Greifswald and the surrounding territory (Vorpommern) were under Swedish rule. In 1815 it came to Prussia. During Worpitzky's stay at the University of Greifswald the Ordinarius in mathematics was Johann August Grunert (1797-1872) who succeeded Johann Karl Fischer (1761-1833) in '33 and was succeeded by Bernhard Minningerode (1837-1896) in '74.

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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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