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3a and 3b 3c and 3d admissible Riccati equation An(z analytic functions Analytic Theory approximant for Figures approximant of 1.15 Approximation Theory Arctan(w asymptotic Berlin Bn(z branch point compact subsets compute continued fraction coefficient contour maps convergence of continued converges uniformly corresponding cross-ratio defined deg Vn denote differential equations Dn(z Edited elements Figures 3a finite formal power series formula fraction solution gamma functions given Greifswald Grunert Gymnasium interpolation point Kriegsakademie Lecture Notes level curves linear fractional transformations Mathematik multipoint Njastad obtained Pad6 approximants Pade polynomials positive continued fraction Proceedings professor Proof R-functions rational functions recurrence relation satisfy Schellbach Schur algorithm sequence series expansion significant digits Stieltjes Stieltjes transforms tail sequences tails Theorem Theory of Continued transformation Trondheim Un(z uniformly on compact values Vn(z W.J. Thron Waadeland Weierstrass Worpitzky Worpitzky's z-ap zero