| 释义 |
Asymptotic SeriesAn asymptotic series is a Series Expansion of a Function in a variable  which may converge or diverge (Erdelyi1987, p. 1), but whose partial sums can be made an arbitrarily good approximation to a given function for large enough . Toform an asymptotic series  of , written
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 . If a function has an asymptotic expansion, the expansion is unique. The symbol  is also used to mean directly Similar.
References
 Asymptotic SeriesAbramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 15, 1972. Arfken, G. ``Asymptotic of Semiconvergent Series.'' §5.10 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 339-346, 1985. Bleistein, N. and Handelsman, R. A. Asymptotic Expansions of Integrals. New York: Dover, 1986. Copson, E. T. Asymptotic Expansions. Cambridge, England: Cambridge University Press, 1965. de Bruijn, N. G. Asymptotic Methods in Analysis, 2nd ed. New York: Dover, 1982. Dingle, R. B. Asymptotic Expansions: Their Derivation and Interpretation. London: Academic Press, 1973. Erdelyi, A. Asymptotic Expansions. New York: Dover, 1987. Morse, P. M. and Feshbach, H. ``Asymptotic Series; Method of Steepest Descent.'' §4.6 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 434-443, 1953. Olver, F. W. J. Asymptotics and Special Functions. New York: Academic Press, 1974. Wasow, W. R. Asymptotic Expansions for Ordinary Differential Equations. New York: Dover, 1987.
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