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Asymptotic developments. I: Fundamental theorems of asymptotics. (English) Zbl 0075.04901


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[1] Proceedings, Series A57 (1954), 206–217: A58 (1955), 139–150; A59 (1956), 1–10; 11–14; 129–142. The same summaries have been published in Indagationes Mathematicae,16 (1954), 206–217;17 (1955), 139–150;18 (1956), 1–10; 11–14; 129–142.
[2] H. Poincaré, Sur les intégrales irrégulières des équations linéaires, Acta Mathematica8, 1886, 295–344. · JFM 18.0273.02 · doi:10.1007/BF02417092
[3] H. Poincaré, Sur les intégrales irrégulières des équations linéaires, Acta Math.8, 1886, 295–344. · JFM 18.0273.02 · doi:10.1007/BF02417092
[4] Hj. Mellin, Abriss einer allgemeinen und einheitlichen Theorie der asymptotischen Reihen, Wissenschaftliche Vorträge gehalten auf dem fünften Kongress der Skandinavischen Mathematiker in Helsingfors, 1922, p. 1–17.
[5] H. Schmidt, Beiträge zu einer Theorie der allgemeinen asymptotischen Darstellungen, Math. Annalen113, 1937, 629–656. · Zbl 0016.20801 · doi:10.1007/BF01571655
[6] J. Popken, Asymptotic expansions from an algebraic standpoint, Proc. Royal Neth. Academy of Sciences, Amsterdam, Series A56, 1953, 131–143; Indagationes Mathematicae15, 1953, 131–143 · Zbl 0051.04803
[7] See for instance, T. Carleman, Les fonctions quasi analytiques. Collection Borel, Paris 1926, 116 pages. S. Mandelbrojt, Séries de Fourier et classes quasi-analytiques, Collection Borel, Paris 1935.
[8] Ricardo San Juan, Les fondements d’une théorie générale des séries divergentes. Revista de Faculdade de Ciências, Serie (2), A,2, 1952, 45–76, with a bibliography. The same volume contains his paper: Condiciones suficientes de prolongación radial, p. 185–194. Sobre la existencia de una función holomorfa que se aproxime asintóticamente a una serie dada con cotas prefijadas, y de una función real indefinidamente derivable en un intervalo con derivadas prefijadas en un punto y acotadas en el intervalo, Collectanea Math.4, 1951, 83–91. Algunos desarrolos asintoticos notables, Revista Matematica Hispano-Americana, Serie (4),11, 1951, 65–110. Algunos teoremas sobre derivación de series asintoticas potenciales, Collectanea Math.,5, 1952. Analisis de dos series estudiadas por Hardy, Revista Matematica Hispano-Americana, Serie (4),13, 1953, 128–144.
[9] See l.c., p. 637.
[10] Robert L. Evans, Errors in asymptotic solutions of linear ordinary differential equations, Quarterly of applied Mathematics,12, 1954, 295–300. · Zbl 0058.07005
[11] E. Borel, Sur quelques points de la théorie des fonctions. Thèse, Annales de l’École Normale 1895.
[12] T. Carleman, Ueber die Approximation analytischer Funktionen durch lineare Aggregate von vorgegebenen Potenzen, Arkiv för Matematik, Astronomi och Fysik, Stockholm,17, 1923, No. 9; 30 pages. T. Carleman, Les fonctions quasi analytiques, Paris, Gauthier-Villars, 1926; 116 pages; see p. 37–40.
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