asymptotic expansion

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asymptotic expansion

[ā‚sim′täd·ik ik′span·shən]
(mathematics)
A series of the form a0+ (a1/ x) + (a2/ x 2) + · · · + (an / xn) + · · · is an asymptotic expansion of the function f (x) if there exists a number N such that for all nN the quantity xn [f (x) -Sn (x)] approaches zero as x approaches infinity, where Sn (x) is the sum of the first n terms in the series. Also known as asymptotic series.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Because the coefficients [a.sub.n] depend of z, (1.8) is not a genuine Poincare expansion, but the terms of the expansion can be grouped to obtain a genuine Poincare expansion .
Then, (2.13) is not a genuine Poincare expansion. But we can group the terms of (2.13) in such a way that we get a genuine Poincare expansion,
Nevertheless, the terms of the expansion [[SIGMA].sub.m] [h.sub.m,n-sm](z) [[PHI].sub.m,n-sm](z) can be grouped in new terms [[psi].sub.n](z) and the new asymptotic expansion [[SIGMA].sub.n] [[psi].sub.n](z) is a genuine Poincare expansion, [[psi].sub.n](z) = O([z.sup.-n-p]) as z [right arrow] [infinity].

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