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

Contents: S.C. Cooper: -Fraction strategies 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 persevered Fractions and his Times.- W.B. Jones, N.J. Wyshinski: confident T-Fraction Expansions for a family members of certain Functions.- J.H. McCabe: On endured Fractions linked to Polynomial sort 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 persisted Fraction Expansions.- W.J. Thron: persevered 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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Extra resources for Analytic Theory of Continued Fractions III: Proceedings of a Seminar-Workshop, held in Redstone, USA, June 26–July 5, 1988

Sample text

Grunert, who was Ordinarius at Greifswald, had been interested in continued fractions and probably had suggested at least the Riccati investigation to Worpitzky. He also had at least one student who wrote a thesis on convergence of continued fractions under him. This was Fr. Arndt in '45. Arndt was at that time a teacher in Stralsund. Later he was a lecturer and eventually an associate professor at UB. Worpitzky may have had a falling out with Grunert. Otherwise it would appear to be strange that Worpitzky published in the Archly.

T h e o r e m 2 . 2 b Let/3 < 0, 0 < a < [BI and a positive integer n be given. Let ~n(t) := n(t - / 3 ) ~ , - a - / 3 < t < - ~ . aa 1 {-(-~)-~-'~nO - ,~) + 2(-~)- ~-' Z j=o ,t-tl T ~ . { 2 j + 1 \ 11(~) ~ ~ ~s s,nt - - - - ~ ) , , / j ° , j=o i f n is odd. 2a). 2d) is obtalned. , k # o, and v = - n ( - , O - ~)~. Remark. 2c) is used to compute ct` for negative k < - 2 . ) + 17G27(~-~)--a + ' " , i f o < ~ < _ I~1, ~ 0 and with z = ~ - ~ , f , , , ( ~ -/~) have asymptotic properties of G(n, ~ ol 1 - ~) about w = 0 and w = ( ~ ) ~ , in the sense that and ~-~)-/,,,(~-~) = , w--,o, for z E D ( ~ , a + ~).

Gm(z)-gm-~(z))l, [C(z) - go,(z)l < - i f 0 < [arg(z)] < 2; 7r esclarg(z)[[(g,~(z) - g,~-l(z))F, i f ~ < larg(z)[ < ~r. 12a) is the straight line segment from 0 to w. 2) can be obtained. 3. 8). 3. 14) where in each case we consider the principal branch. For each function we give numerical values of the moments eL and coefficients Ft and Gl. These coefficients are used to compute level curves of the number of significant digits S D ( f , , ( a , ~ , n , w)) obtained in the approximation of F ( n , w ) by an m - t h approximant f r a ( a , ~ , n , w ) of the positive T-fraction.

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