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 REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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BOSHERNITZAN, M. An extension of Hardy's class L of 'Orders of infinit,y'. J. Analyse Math 39 (1981), 235- 255.
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2
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BOSHERNITZAN, M. New 'Orders of Infinity'. J. Analyse Math. 41 (1982), 130 167.
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BOSHERNITZAN, M. Hardy fields, existence of transexponential functions and the hypertralscendence of solution to g(g(x)) = ex. Aequationes Math. 30 (1986), 258-280.
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BOSHERNITZAN, M. Second-order differential equations over Hardy fields. J. London Math. Soc. 35 (1987), 109 120.
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5
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BOURBAKI, N. ~l~ments de Math~matiques. Ch. V: Fonctions d'une variable r~elle. Appendice, pp. 36 55. Hermann. Paris, Second edition, 1961.
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BROMWlCH, T. An Introduction to the Theory of lnfinitc Series, 2nd ed. Macmillan, 1926.
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DE BRUIJN, N. Asymptotic Methods in Analysis. North Holland, 1958.
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ECALLE, J. Introduction aux fontions analysables et preuve constructive de la conjecture, de Dulac. Hermann, Paris, 1992.
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HARDY, G. Orders of lnfinity. Cambridge Univ. Press, Cambridge, England, 1910.
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KUHLMANN, S. Ordered Exponential Fields. University of Saskatchewan, Canada S7N 5E6, 1998. Habilitationsschrift, University of Heidelberg.
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L. VAN DEN DRIES, MAClNTYRE AND D. MARKER. Logarithmic-exponential power series. Tech. rep., University of Illinois, 1995.
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12
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LIGHTSTONE, A., AND ROBINSON, A. Nonarchimedean Fields and Asymptotic Expansions. Elsevier, New York, 1975.
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RAMIS, J., AND MARTINET, J. Th~orie de Galois Diff~rentielle et resommation. In Computer Algebra and Differential Equations (1989), E. Tournier, Ed., Academic Press, pp. 117 214.
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14
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RICHARDSON, D. Some undecidable problems involving elementary functions of a real variable. J. Symbolic Logic 33 (1968), 514-520.
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Daniel Richardson , Bruno Salvy , John Shackell , Joris Van der Hoeven, Asymptotic expansions of exp-log functions, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.309-313, July 24-26, 1996, Zurich, Switzerland
[doi> 10.1145/236869.237089]
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ROBINSON, A. On the real closure of a Hardy field. In Theory of Sets and Topology (Berlin, 1972), G. A. et al., Ed.. Deut. Verlag Wissenschaften.
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ROSENLIGHT, M. Differential valuations. Pacific J. Math 86 (1980), 301-319.
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ROSENLIGHT, M. Hardy fields. J. Math. Anal. App. 93/2 (1983), 297-311.
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ROSENLIGHT, M. The rank of a Hardy field. Trans. Amer. Math. Soc. 280/2 (1983), 659-671.
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ROSENLIGHT, M. Rank change on adjoining real powers to Hardy fields. Trans. Amer. Math. Soc. 284/2 (1984), 829.836.
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ROSENLIGHT, M. Growth properties of functions in Hardy fields. Trans. Amer. Math. Soc. 299/1 (1987), 261-272.
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SALVY, B., AND SHACKELL, J. Symbolic asymptotics: Multiseries for inverse functions. Tech. rep., INRIA France & University of Kent at Canterbury, U.K., 1997. INRIA Research report 3264, Technical Report UKC/IMS/97/49.
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SHACKELL, J. Rosenlicht fields. Trans. Amer. Math. Soc. 335/2 (1993), 579 595.
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SHACKELL, J. Limits of Liouvillian functions. Proc. London Math. Soc. 72 (1996), 124-156.
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SHACKELL, J. Star products 2: Growth Classes in Hardy fields. Tech. rep., University of Kent at Canterbury, England, 1999. Technical report UKC-IMS/99/05.
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