Nested expansions and hardy fields

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Nested expansions and hardy fields

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1993 international symposium on Symbolic and algebraic computation table of contents

Kiev, Ukraine

Pages: 234 - 238

Year of Publication: 1993

ISBN:0-89791-604-2

Author

John Shackell

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

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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.

	1	M. Boshernitzan. An extension of Hardy's class L of 'Orders of infinity'. J. Analyse Math, 39:235- 255, 1981.
	2	M. Boshernitzan. New 'Orders of Infinity'. J. Analyse Math., 41:130-167, 1982.
	3	M. Boshernitzan. Hardy fields, existence of transexponential functions and the hypertranscendence of solution to g(g(x)) = e~. Aequationes Math., 30:258-280, 1986.
	4	M. Boshernitzan. Second-order differential equations over Hardy fields. J. London Math. Soc., 35:109-120, 1987.
	5	N. Bourbaki. Eldments de Mathdmatiques. Ch. V: Fonctions d'une variable rdelle. Appendice, pp. 36- 55. Hermann, Paris, Second edition, 1961.
	6	T.J.I'A Bromwich. An Introduction to the Theory of Infinite Series, 2nd ed. Macmillan, 1926.
	7	B.I. Dahn and P. G5ring. Notes on exponentiallogarithmic terms. Fundamenta Math., 127:45-50, 1986.
	8	N.G. de Bruijn. Asymptot2c Methods in Analysis. North Holland, 1958.
	9	J. Denef and L. Lipshitz. Power series solutions of algebraic differential equations. Math. Ann., 267:213-238, 1984.
	10	G.H. Hardy. Properties of logarithmicoexponential functions. Proc. London Math. Soc., 10:54-90, 1912.
	11	G.H. Hardy. Divergent Series. Oxford Univ. Press, 1949.
	12	A. Lightstone and A. Robinson. Nonarchimedean Fields and Asymptotic Expansions. Elsevier, New York, 1975.
	13	F. Olver. Asymptotics and Special Functions. Academic Press, 1974.
	14	J.P. Ramis and J. Martinet. Th~orie de Galois Diff~rentielle et resommation. In E. Tournier, editor, Computer Algebra and Differential Equatzons, pages 117-214. Academic Press, 1989.
	15	A. Robinson. On the real closure of a Hardy field. in G. Asser et al., editor, Theory of Sets and Topology, Berlin, 1972. Deut. Verlag Wissenschaften.
	16	M. Rosenlicht. Hardy fields. J. Math. Anal. App., 93/2:297-311, 1983.
	17	M. Rosenlicht. The rank of a Hardy field. Trans. Amer. Math. Soc., 280/2:659-671, 1983.
	18	M. Rosenlicht. Rank change on adjoining real powers to Hardy fields. Trans. Amer. Math. Soc., 284/2:829-836, 1984.
	19	M. Rosenlicht. Growth properties of functions in Hardy fields. Trans. Amer. Math. Soc., 299/1:261- 272, 1987.
	20	L. A. Rubel. A universal differential equation. Bull. Amer. Math. Soc., 4(N.S.):345-349, 1981.
	21	Bruno Salvy , John Shackell, Asymptotic expansions of functional inverses, Papers from the international symposium on Symbolic and algebraic computation, p.130-137, July 27-29, 1992, Berkeley, California, United States [doi>10.1145/143242.143292]
	22	J. Shackell, Growth estimates for exp-log functions, Journal of Symbolic Computation, v.10 n.6, p.611-632, Dec. 1990 [doi>10.1016/S0747-7171(08)80161-7]
	23	J.R. Shackell. Limits of Liouvillian functions. Technical report, University of Kent at Canterbury, England, 1991.
	24	J.R. Shackell. Extensions of asymptotic fields via meromorphic functions. Technical report, University of Kent at Canterbury, England, 1992. Provisionally accepted by J. London Math. Soc.
	25	J.R. Shackell. Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations. Technical report, University of Kent at Canterbury, England, 1992. In preparation.
	26	J.R. Shackell. Inverses of Hardy L-functions. Technical report, University of Kent at Canterbury, England, 1992. To be published in Bull. London Math. Soc.
	27	J.R. Shackell. Rosenlicht fields. Trans. Amer. Math. Soc., 335/2:579-595, 1993.
	28	J.R. Shackell and B. Salvy. Asymptotic forms and algebraic differential equations. Technical report, University of Kent at Canterbury, England, 1992.
	29	Michael F. Singer, Formal solutions of differential equations, Journal of Symbolic Computation, v.10 n.1, p.59-94, July 1990 [doi>10.1016/S0747-7171(08)80037-5]
	30	W. Strodt. A differential algebraic study of the intrusion of logarithms into asymptotic expansions. In P.J. Cassidy H. Bass and J. Kovacic, editors, Contributions to Algebra, pages 355-375. Academic Press, 1977.
	31	W. Wasow. Asymptotic Expansions for Ordinary Differential Equations. Dover Publications Inc., 1965.