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An analysis of the impact of T. M. Cherry's work on asymptotic expansions

Published online by Cambridge University Press:  17 February 2009

R. Grimshaw
Affiliation:
School of Mathematics, University of N.S.W., P.O. Box 1 Kensington, N.S.W. 2033, Australia.
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Abstract

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During the late 1940s, T. M. Cherry published a series of research papers on uniform asymptotic formulae for transition points in ordinary differential equations. This work, together with his research into transonic gas flows, for which it was a necessary precursor, is probably his best known and most widely quoted piece of research. An analysis is made of the impact of Cherry's work on subsequent developments in this field, both in comparison to the work of others and with respect to Cherry's work on other topics.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bullen, K. E. and Temple, G., “Thomas MacFarland Cherry, 1898–1966“, Biog. Mem. Fellows Roy. Soc. 14. (1968) 117.Google Scholar
[2]Cesari, L., Asymptotic behavior and stability in ordinary differential equations (Springer, Berlin, 1962).Google Scholar
[3]Copson, E., Asymptotic expansions (CUP, Cambridge, 1965).CrossRefGoogle Scholar
[4]Dingle, R., Asymptotic expansions: their derivation and interpretation (Academic Press, New York, 1973).Google Scholar
[5]de Bruijn, N., Asymptotic methods in analysis (North-Holland, Amsterdam, 1958).Google Scholar
[6]Erdèlyi, A., Asymptotic Expansions (Dover, New York, 1956).Google Scholar
[7]Jeffreys, H., Asymptotic Approximations (Dover, New York, 1962).Google Scholar
[8]Langer, R. E., Trans. Amer. Math. Soc., 33 (1931) 23.CrossRefGoogle Scholar
[9]Langer, R. E., Trans. Amer. Math. Soc., 34 (1932) 447.Google Scholar
[10]Langer, R. E., Trans. Amer. Math. Soc., 67 (1949) 461.Google Scholar
[11]Love, E. R., “Thomas MacFarland Cherry”, J. Aust. Math. Soc., 9 (1969) 1.Google Scholar
[12]McHugh, J. A. M., Arch. Hist. E. Sc., 7 (1971) 277.Google Scholar
[13]Olver, F. W. J., Phil. Trans. Roy. Soc., A 247 (1954) 307, 328.Google Scholar
[14]Olver, F. W. J., Asymptotics and special functions (Academic, New York, 1974).Google Scholar
[15]Sirovich, L., Techniques of asymptotic analysis (Springer, Berlin, 1971).Google Scholar
[16]Thorne, R. C., Phil. Trans. Roy. Soc. A 249 (1957) 585, 597.Google Scholar
[17]Wasow, W., Asymptotic expansions for ordinary differential equations (Interscience, New York, 1965).Google Scholar
[18]Zauderer, E., Proc. Amer. Math. Soc., 31 (1972) 489.Google Scholar
[19]Zauderer, E., J. Chem. Phys., L 56 (1972) 5198.Google Scholar