Limits of Liouvillian functions

Proceedings of the London Mathematical Society

Volumn 72, Issue 1, 1996, Pages 124-156

  Shackell, John ^a  

^a UNIVERSITY OF KENT   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010144028     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/plms/s3-72.1.124     Document Type: Article

References (28)

1. M. BOSHERNITZAN, 'An extension of Hardy's class L of "Orders of Infinity"', J. Analyse Math. 39 (1981) 235-255.
2. N. BOURBAKI, Éléments de mathématiques. Chapitre V: Fonctions d'une variable réelle, 2nd edn (Hermann, Paris, 1961), Appendice, pp. 36-55.
3. B. I. DAHN and P. GÖRING, 'Notes on exponential-logarithmic terms', Fundamenta Math. 127 (1986) 45-50.
4. J. H. DAVENPORT, On the integration of algebraic functions (Springer, Berlin, 1981).
5. N. G. DE BRUIJN, Asymptotic methods in analysis (North Holland, Amsterdam, 1958).
6. K. O. GEDDES and G. H. GONNET, 'A new algorithm for computing symbolic limits using hierarchical series', ISSAC88 Proceedings, Rome, 1988 (ed. P. Gianni, Springer, Berlin, 1989), pp. 490-495.
7. D. GRUNTZ, 'A new algorithm for computing asymptotic series', ISSAC93 Proceedings, Kiev, 1993 (ed. M. Bronstein, A.C.M., New York, 1993), pp. 239-244.
8. G. H. HARDY, Orders of infinity (Cambridge University Press, 1910).
9. G. H. HARDY, 'Properties of logarithmico-exponential functions', Proc. London Math. Soc. (2) 10 (1912) 54-90.
10. I. KAPLANSKY, An introduction to differential algebra (Hermann, Paris, 1957).
11. S. LANG, Algebra (Addison-Wesley, Reading, Mass., 1965).
12. A. J. MACINTYRE, 'The laws of exponentiation', Model theory and arithmetic (eds C. Berline, K. McAloon, and J. P. Rossayre, Springer, Berlin, 1981), pp. 185-197.
13. A. C. NORMAN, 'Computing in transcendental extensions', Computer algebra: symbolic and algebraic computation, 2nd edn (eds B. Buchberger, G. E. Collins and R. Loos, Springer, New York, 1983), pp. 11-43.
14. D. RICHARDSON, 'Solution of the identity problem for integral exponential functions', Z. Math. Logik. Grundlag. Math. 15 (1969) 333-340.
15. D. RICHARDSON, 'Computing the topology of a bounded non-algebraic curve in the plane', J. Symbolic Comput. 14 (1992) 619-643.
16. A. ROBINSON, 'On the real closure of a Hardy field', Theory of sets and topology (eds G. Asser et al., Deutscher Verlag der Wissenschaften, Berlin, 1972).
17. M. ROSENLICHT, 'Hardy fields', J. Math. Anal. Appl. 93 (1983) 297-311.
18. M. ROSENLICHT, 'The rank of a Hardy field', Trans. Amer. Math. Soc. 280 (1983) 659-671.
19. M. ROSENLICHT, 'Rank change on adjoining real powers to Hardy fields', Trans. Amer. Math. Soc. 284 (1984) 829-836.
20. M. ROSENLICHT, 'Growth properties of functions in Hardy fields', Trans. Amer. Math. Soc. 299 (1987) 261-272.
21. J. R. SHACKELL, 'A differential-equations approach to functional equivalence', ISSAC89 Proceedings, Portland, Oregon, 1989 (ed. G. Gonnet, A.C.M. Press, New York, 1989), pp. 7-10.
22. J. R. SHACKELL, 'Growth estimates for exp-log functions', J. Symbolic Comput. 10 (1990) 611-632.
23. J. R. SHACKELL, 'Computing asymptotic expansions of Hardy fields', Technical report, University of Kent at Canterbury, 1991.
24. J. R. SHACKELL, 'Extensions of asymptotic fields via meromorphic functions', J. London Math. Soc. to appear.
25. J. R. SHACKELL, 'Rosenlicht fields', Trans. Amer. Math. Soc. 335 (1993) 579-595.
26. J. R. SHACKELL, 'Zero-equivalence in function fields defined by algebraic differential equations', Trans. Amer. Math. Soc. 336 (1993) 151-172.
27. J. R. SHACKELL and B. SALVY, 'Asymptotic forms and algebraic differential equations', Technical report, University of Kent at Canterbury, 1992.
28. M. SINGER, 'An outline of differential galois theory', Computer algebra and differential equations (ed. E. Tournier, Academic Press, New York, 1989), pp. 3-57.