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.
References in periodicals archive ?
In 1985, the theory made a huge progress via an asymptotic expansion produced by Matsuoka [21], for these constants.
From this, we could obtain more terms and better error terms of the asymptotic expansion of the expected value, the variance and higher moments.
In [14], we constructed an asymptotic expansion of the expectation of g([x.
In [6] the author proposed to interpolate band-limited functions using PSWF, however, did not present a concrete reconstruction scheme though he did state that PWSF are mathematically intractable and presented asymptotic expansion.
The asymptotic expansion of the solution and the associated truncation errors have been deeply investigated in [6-8].
In a very recent study [9], using an asymptotic expansion technique, the asymptotic equations governing unidirectional wave propagation of small-butfinite amplitude long waves in the nonlinear nonlocal elastic medium were derived.
The drawback of this can eliminate by the use of higher order terms [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in asymptotic expansion [24, 25].
1973 "An Asymptotic Expansion of the Distribution of Studentized Classification Statistic" (Annals of Statistics, Vol.
Mansour [12] derived an asymptotic expansion of the q-gamma function [[GAMMA].
Debby asymptotic expansion of the Hankel function is written as
Also, as the frequency increases beyond a few tens of GHz for dimensions in the mm range, one needs to consider even the third order term in the asymptotic expansion for the Green's function if faster convergence is required in the value of the propagation constant.

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