Upon the Padé Table Derived from a Stieltjes Series

Abstract

Previous article Next article Upon the Padé Table Derived from a Stieltjes SeriesPeter WynnPeter Wynnhttps://doi.org/10.1137/0705060PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Pringsheim, Über die Convergenz unendlicher Kettenbrüche, Sitzungsber. der math.-phys. Klasse der Kgl. Bayer. Akad. Wiss., 28 (1898), 295–324 Google Scholar[2] Oskar Perron, Die Lehre von den Kettenbrüchen. Dritte, verbesserte und erweiterte Aufl. Bd. II. Analytisch-funktionentheoretische Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1957vi+316 MR0085349 0077.06602 Google Scholar[3] G. Hankel, Masters Thesis, Über eine besondere Klasse der symmettrischen Determinanten, Leipzig dissertation, University of Göttingen, 1861 Google Scholar[4] H. Padé, Sur la représentation approchée d'une fonction par des fractions rationnelles, Ann. Sci. École Norm. Sup. (3), 9 (1892), 3–93 MR1508880 24.0360.02 CrossrefGoogle Scholar[5] T.-J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys., 8 (1894), J1–J122 MR1508159 25.0326.01 CrossrefGoogle Scholar[6] T. Carleman, Les fonctions quasi-analytiques, Gauthier-Villars, Paris, 1923 Google Scholar[7] Edward Burr Van Vleck, On an extension of the 1894 memoir of Stieltjes, Trans. Amer. Math. Soc., 4 (1903), 297–332 MR1500644 34.0247.01 CrossrefGoogle Scholar[8] J. J. Sylvester, A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares, Philos. Mag., ser. 4, 4 (1852), 140–141 Google Scholar[9] J. Hadamard, Essai sur l'étude des fonctions données par leur développement de Taylor, J. Math. Pures Appl., 8 (1892), 101–186 24.0359.01 Google Scholar[10] A. Markov, Deux demonstrations de la convergence de certaines fractions continues, Acta. Math., 19 (1895), 93–104 26.0234.01 CrossrefGoogle Scholar[11] R. de Montessus, Sur les fractions continues algébriques, Bull. Soc. Math. France, 30 (1902), 28–36 MR1504403 33.0227.01 CrossrefGoogle Scholar[12] Hubert S. Wall, On the Padé approximants associated with the continued fraction and series of Stieltjes, Trans. Amer. Math. Soc., 31 (1929), 91–116 MR1501470 55.0271.01 Google Scholar[13] D. R. Hartree, Numerical analysis, Oxford, at the Clarendon Press, 1952xiv+287 MR0052871 0049.35905 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The Legacy of Peter Wynn28 May 2021 | Mathematics, Vol. 9, No. 11 Cross Ref The Mathematical Landscape up to the Mid-Twentieth Century1 December 2020 Cross Ref The Works of Peter Wynn1 December 2020 Cross Ref Reminiscences of Peter Wynn10 May 2018 | Numerical Algorithms, Vol. 80, No. 1 Cross Ref A rigorous foundation of the diffusion-influenced bimolecular reaction kineticsThe Journal of Chemical Physics, Vol. 131, No. 1 Cross Ref Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problemsComputer Physics Communications, Vol. 133, No. 2-3 Cross Ref The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformationsJournal of Mathematical Physics, Vol. 34, No. 2 Cross Ref Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent seriesComputer Physics Reports, Vol. 10, No. 5-6 Cross Ref Pade approximants and the calculation of spectral functions of solids24 November 2000 | Journal of Physics C: Solid State Physics, Vol. 15, No. 7 Cross Ref THE TRANSFORMATION OF SERIES BY THE USE OF PADÉ QUOTIENTS AND MORE GENERAL APPROXIMANTS Cross Ref Computation of Padé approximants and continued fractionsJournal of Computational and Applied Mathematics, Vol. 2, No. 2 Cross Ref Generalisations de la transformation de shanks, de la table de Pade et de l'ε-algorithmeCalcolo, Vol. 12, No. 4 Cross Ref Extremal properties of Padé quotientsActa Mathematica Academiae Scientiarum Hungaricae, Vol. 25, No. 3-4 Cross Ref Rationale Interpolation, Normalit�t und MonosplinesNumerische Mathematik, Vol. 22, No. 3 Cross Ref Numerical analytic continuation using Padé approximantsJournal of Computational Physics, Vol. 13, No. 1 Cross Ref The Padé Table and Its Relation to Certain Algorithms of Numerical AnalysisW. B. Gragg18 July 2006 | SIAM Review, Vol. 14, No. 1AbstractPDF (3619 KB) Volume 5, Issue 4| 1968SIAM Journal on Numerical Analysis History Submitted:22 March 1968Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705060Article page range:pp. 805-834ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics